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FrB1 |
Room 2463 |
Coding Theory: Coding Theory and Applications |
Invited Session |
Chair: Westerbäck, Thomas | Aalto Univ |
Co-Chair: Ravagnani, Alberto | Univ. Coll. Dublin |
Organizer: Han, Guangyue | The Univ. of Hong Kong |
Organizer: Pinto, Raquel | Univ. of Aveiro |
Organizer: Rosenthal, Joachim | Univ. of Zurich |
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10:30-10:55, Paper FrB1.1 | |
>On the Polymatroidal Structure of Quasi-Uniform Codes with Applications to Heterogeneous Distributed Storage (I) |
Westerbäck, Thomas | Aalto Univ |
Grezet, Matthias | Aalto Univ |
Freij-Hollanti, Ragnar | Tech. Univ. of Munich |
Hollanti, Camilla | Aalto Univ |
Keywords: Coding Theory, Information Theory, Communication Systems
Abstract: Recent research on distributed storage systems (DSSs) has revealed interesting connections between locally repairable codes (LRCs) and their associated matroids and polymatroids. In this paper we define L-polymatroids - polymatroids with an added length function - in order to consider completely general LRCs in that they are defined as subsets of A^E = A_1 x ... x A_n, where each A_i is some arbitrary finite set. Earlier research in this area has only considered codes over non-mixed alphabets, i.e., A_1 = ... = A_n.
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10:55-11:20, Paper FrB1.2 | |
>Matrix Codes with the Rank-Metric and Their Covering Radii (I) |
Ravagnani, Alberto | Univ. Coll. Dublin |
Byrne, Eimear | Univ. Coll. Dublin |
Keywords: Coding Theory, Information Theory, Communication Systems
Abstract: The covering radius of a rank-metric code is defined as the maximum distance between the code and a matrix from the ambient space. This fundamental parameter measures the performance of a code both in error correction and source coding applications. In this paper we discuss some structural properties of matrix codes endowed with the rank metric, and relate them to the covering radius. In particular, we derive upper bounds on the covering radius of a rank-metric code by applying different combinatorial methods.
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11:20-11:45, Paper FrB1.3 | |
>A Simple State-Space Realization Method for a Class of Periodic Encoders (I) |
Pereira, Ricardo | Univ. of Aveiro |
Rocha, Paula | Univ. of Porto |
Napp, Diego | Univ. of Aveiro |
Keywords: Coding Theory, Linear Systems
Abstract: Convolutional codes are an important type of error correcting codes that can be represented as a time-invariant discrete linear system over a finite field . Since the seminal work of Costello, time-varying convolutional codes raised a great interest as they can attain larger free distance than the time-invariant ones with equivalent parameters. In this work we aim at investigating time-varying convolutional codes from a system theoretical point of view. In particular, we study the realization of periodic encoders by means of periodic state-space models with the aim of efficient implementation. More concretely, in this preliminary work we focus on period two and investigate under which conditions a given periodic encoder obtained by alternating two time-invariant encoders can be realized by a periodic state-space system. We first observe that, in general, one cannot expect to obtain a periodic state-space realization by means of the individual realizations of each associated time-invariant encoders. However, we give conditions for such procedure to hold. The presented results are illustrated by examples.
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11:45-12:10, Paper FrB1.4 | |
>A New Metric for Multi-Shot Network Coding (I) |
Napp, Diego | Univ. of Aveiro |
Requena, Veronica | Univ. of Alicante |
Climent, Joan-Josep | Univ. of Alicante |
Keywords: Coding Theory, Information Theory, Communication Systems
Abstract: In this paper we study convolutional codes in the context of multi-shot network coding. Within this context, several classes of rank metric convolutional codes have been recently proposed in the literature. The metric considered so far in this context is the so-called sum rank distance, which makes the unnecessary assumption that the natural delay in the transmission (due, for instance, to the delay of the nodes) is so small that can be disregarded. In this work we introduce a new metric that overcomes this restriction and therefore is suitable to handle networks with delays. We shall call it the column rank distance.
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FrB2 |
Room 2464 |
Further Developments and Applications of Multidimensional Systems |
Invited Session |
Chair: Galkowski, Krzysztof | Univ. of Zielona Gora |
Co-Chair: Azevedo Perdicoulis, Teresa Paula | ISR-Coimbra & UTAD |
Organizer: Galkowski, Krzysztof | Univ. of Zielona Gora |
Organizer: Azevedo Perdicoulis, Teresa Paula | ISR-Coimbra & UTAD |
Organizer: Rocha, Paula | Univ. of Porto |
Organizer: Rogers, Eric | Univ. of Southampton |
Organizer: Pakshin, Pavel | Nizhny Novgorod State Tech. Univ |
Organizer: Patan, Maciej | Univ. of Zielona Gora |
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10:30-10:55, Paper FrB2.1 | |
>A Finite Difference Scheme for Iterative Learning Control Oriented Modelling of Physical Systems Described by PDEs in Polar Coordinates (I) |
Augusta, Petr | Czech Acad. of Sciences |
Cichy, Blazej | Univ. of Zielona Gora |
Galkowski, Krzysztof | Univ. of Zielona Gora |
Rogers, Eric | Univ. of Southampton |
Keywords: Stability
Abstract: Iterative learning control is a well established area of research and application, with a relatively short time between the development of the theory and design algorithms and experimental validation. This form of control is especially suitable for applications where the system is required to make repeated executions of a finite duration task with resetting to the starting location at the end of each execution. The majority of the theory and designs are for systems described by finite dimensional differential or discrete systems but there is increasing interest in the extension to systems described by partial differential equations, where for most applications, approximate finite dimensional models of the dynamics are required. The construction of such models is the subject of this paper, where the developments are in terms of systems whose dynamics are described by a fourth-order partial differential equation and the use of regular hexagonal grid and polar coordinates. The scheme is motivated by the well-known Crank-Nicolson discretization that was originally developed for first-order systems and the stability of the resulting finite-difference scheme is analyzed by von Neumann method. Using the new scheme, a discrete in time and space model of a deformable mirror is derived as the basis for control law design. The convergence of this scheme for various values of the discretization parameters is checked by numerical simulations.
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10:55-11:20, Paper FrB2.2 | |
>Converse Stability Theorems for 2D Systems (I) |
Pakshin, Pavel | Nizhny Novgorod State Tech. Univ |
Emelianova, Julia | Arzamas Pol. Inst. of R.E. Alekseev Nizhny Novgorod S |
Galkowski, Krzysztof | Univ. of Zielona Gora |
Rogers, Eric | Univ. of Southampton |
Keywords: Nonlinear Systems and Control, Stability, Multidimensional Systems
Abstract: The paper considers 2D discrete nonlinear systems described by either the Fornasini-Marchesini or Roesser state-space models. Converse stability theorems are developed, which establish that, if an example is exponentially stable, there exists a vector Lyapunov function with particular properties of its entries and the discrete counterpart of divergence. The extension of these results to some class of stochastic models are also given. Key words: Multidimensional systems, Fornasini-Marchesini model, Roesser model, converse stability theorems, vector Lyapunov functions AMS subject classifications: 93D05, 93D30, 93E15
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11:20-11:45, Paper FrB2.3 | |
>Stability Analysis and Stabilization of the Subclass of Symmetric Spatially Interconnected Systems (I) |
Sulikowski, Bartlomiej | Univ. of Zielona Gora, Inst. Control and Computation Eng |
Galkowski, Krzysztof | Univ. of Zielona Gora |
Rogers, Eric | Univ. of Southampton |
Kummert, Anton | Univ. of Wuppertal |
Keywords: Stability, Multidimensional Systems
Abstract: This paper develops new results on the stability and stabilization of symmetric active ladder circuits, which are a class of spatially interconnected systems. Ladder circuits can be considered as two--dimensional systems constituted as a homogenous (in the node structure and/or in parameters of nodes values) sequence of nodes (or cells) where information is propagated in two separate directions, i.e., along the time axis and along a space variable represented by a node number. In contrast to previous research in this general area, the independent energy source is placed in the center of the ladder. A~new two-dimensional systems state-space model is developed for this case, leading to a new equivalent linear time-invariant model in one indeterminate obtained by applying a form of lifting along the nodes. Using this model description, the problems of stability testing and stabilization are addressed in a linear matrix inequality setting. A numerical case study is also given to illustrate the application of the new results.
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11:45-12:10, Paper FrB2.4 | |
>Reduction of Wave Linear Repetitive Processes to 2-D Singular State Space Form (I) |
Galkowski, Krzysztof | Univ. of Zielona Gora |
Boudellioua, Mohamed S. | Sultan Qaboos Univ |
Keywords: Multidimensional Systems, Algebraic Systems Theory, Linear Systems
Abstract: In this paper, a method is given that reduces a polynomial system matrix describing a discrete wave linear repetitive process to an equivalent 2-D singular Fornasini-Marchesini (SFM) model. It is shown that the transformation linking the original polynomial system matrix with its associated 2-D SFM form is zero coprime system equivalence. The exact nature of the resulting system matrix in singular form and the transformation involved are established.
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12:10-12:35, Paper FrB2.5 | |
>On the State Space Realization of 2D (2, 2)-Periodic Image Behaviors (I) |
Aleixo, José Carlos | Univ. of Beira Interior |
Napp, Diego | Univ. of Aveiro |
Pereira, Ricardo | Univ. of Aveiro |
Pinto, Raquel | Univ. of Aveiro |
Rocha, Paula | Univ. of Porto |
Keywords: Multidimensional Systems
Abstract: In this paper we consider 2D behaviors with periodic image representations and provide conditions under which a simple method for obtaining state space realizations by means of 2D periodic (separable) Roesser models can be applied. For the sake of simplicity we restrict our attention to the (2,2)-periodic case.
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12:35-13:00, Paper FrB2.6 | |
>Comparing Finite Differences Methods for Gas Network Simulation (I) |
Azevedo Perdicoulis, Teresa Paula | ISR-Coimbra & UTAD |
Almeida, Regina | Univ. De Trás-Os-Montes E Alto Douro |
Lopes dos Santos, P. | Univ. Do Porto |
Keywords: Multidimensional Systems, Numerical and Symbolic, Stability
Abstract: This is a study in gas modelling and simulation with a special focus on the simulation of a gas pipeline, the most important element of the network, which is represented by a quasi-hyperbolic PDE, linearised around operational levels. Different numerical schemata are presented for the solution of this problem, explicit and implicit, as well as cell centered discretisation methods. In order to have a well-posed initial-boundary value problem (IBVP), we use two-port network transfer function models to calculate the initial value function. The numerical methods are implemented in Matlab, and we give special relevance to issues as consistency, stability and convergence. Furthermore, we apply each of the schemata to calculate the solution of a pipeline. The present work is part of a research study to evaluate comparatively different numerical methods for the solution of gas network models, in particular the hyperbolic model. We start with a isothermal, one-dimensional gas flow and considering horizontal pipelines.
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FrB3 |
Room 2465 |
Stochastic Approaches and Hamilton-Jacobi Equations |
Invited Session |
Chair: McEneaney, William | Univ. of California, San Diego |
Co-Chair: Kaise, Hidehiro | Osaka Univ |
Organizer: McEneaney, William | Univ. of California, San Diego |
Organizer: Dower, Peter M. | Univ. of Melbourne |
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10:30-10:55, Paper FrB3.1 | |
>Hamilton-Jacobi Partial Differential Equations with Path-Dependent Terminal Costs under Superlinear Lagrangians (I) |
Kaise, Hidehiro | Osaka Univ |
Kato, Takashi | Association of Mathematical Finance Lab |
Takahashi, Yusuke | National Federation of Workers and Consumers Insurance Cooperati |
Keywords: Optimal Control, Nonlinear Systems and Control
Abstract: We consider variational problems with path-dependent terminal costs. Motivated from Mogulskii's theorem in large deviation theory and dynamic importance sampling for path-dependent rare events, we focus on particular forms of Lagrangians with superlinear growth. By reformulating the variational problem to a value function of a path-dependent deterministic control, we study it by path-dependent dynamic programming methods. Under co-invariant derivative notion on path spaces, the value function is related to a Hamilton-Jacobi partial differential equation (PDE) with a path-dependent terminal condition. Using a viscosity type solution proposed by Lukoyanov for a weak notion, we show that the value function can be characterized as a unique viscosity solution of the Hamilton-Jacobi PDE.
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10:55-11:20, Paper FrB3.2 | |
>Solvability of the Non-Linear Dirichlet Problem with Integro-Differential Operators (I) |
Song, Qingshuo | City Univ. of Hong Kong |
Bayraktar, Erhan | Univ. of Michigan |
Keywords: Stochastic Control and Estimation
Abstract: This work studies the solvability of a class of Dirichlet problem associated with non-linear integro-differential operator. The main ingredient is the probabilistic construction of continuous supersolution via the identification of the continuity set of the exit time operators under Skorohod topology.
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11:20-11:45, Paper FrB3.3 | |
>An Action Principle for Constructing Fundamental Solution Groups for Wave Equations (I) |
Dower, Peter M. | Univ. of Melbourne |
McEneaney, William | Univ. of California, San Diego |
Keywords: Infinite Dimensional Systems Theory, Optimal Control
Abstract: By exploiting connections between stationary action and optimal control, fundamental solution groups corresponding to a class of wave equations are constructed via dynamic programming.
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11:45-12:10, Paper FrB3.4 | |
>Convergent Collocation Methods for Hamilton-Jacobi-Bellman Equations (I) |
Nakano, Yumiharu | Tokyo Inst. of Tech |
Keywords: Stochastic Control and Estimation
Abstract: We report a convergence result of kernel-based collocation methods for Hamilton-Jacobi-Bellman equations. In particular, we find the class of kernels and the structure of collocation points explicitly under which the process of iterative interpolation is stable, and show that the functions constructed by the collocation methods converge to a unique viscosity solution of the Hamilton-Jacobi-Bellman equations.
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12:10-12:35, Paper FrB3.5 | |
>Stationarity-Based Representation for the Coulomb Potential and a Diffusion Representation for Solution of the Schrodinger Equation (I) |
McEneaney, William | Univ. of California, San Diego |
Keywords: Stochastic Control and Estimation, Nonlinear Systems and Control, Quantum Control
Abstract: Diffusion representations have long been utilized in the study of Hamilton-Jacobi partial differential equations (HJ PDEs). The bulk of such results apply to real-valued HJ PDEs, that is, to HJ PDEs where the coefficients and solutions are real-valued. The Schrodinger equation is complex-valued, although generally defined over a real-valued space domain, which presents difficulties for the development of stochastic control representations. The approach considered here is in the spirit of the Feynman path-integral interpretation where in particular, one looks at a certain action-based functional. We obtain a representation for the Maslov dequantization of the solution in the form of a value function for a complex-valued diffusion where the action functional is the payoff. Previous efforts required a potential possessing a holomorphic extension. Here, a staticization-based representation for the Coulomb potential is used to bypass such a requirement.
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FrB4 |
Room 2502 |
Networked Control Systems II |
Regular Session |
Co-Chair: Morita, Ryosuke | Gifu Univ |
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10:30-10:55, Paper FrB4.1 | |
>Noise-Induced Limitations to the Scalability of Distributed Integral Control |
Tegling, Emma | KTH Royal Inst. of Tech |
Sandberg, Henrik | KTH Royal Inst. of Tech |
Keywords: Networked Control Systems, Large Scale Systems
Abstract: We study performance limitations of distributed feedback control in large-scale networked dynamical systems. Specifically, we address the question of how the performance of distributed integral control is affected by measurement noise. We consider second-order consensus-like problems modeled over a toric lattice network, and study asymptotic scalings (in network size) of H2 performance metrics that quantify the variance of nodal state fluctuations. While previous studies have shown that distributed integral control fundamentally improves these performance scalings compared to distributed proportional feedback control, our results show that an explicit inclusion of measurement noise leads to the opposite conclusion. The noise’s impact on performance is shown to decrease with an increased inter-nodal alignment of the local integral states. However, even though the controller can be tuned for acceptable performance for any given network size, performance will degrade as the network grows, limiting the scalability of any such controller tuning. In particular, the requirement for inter-nodal alignment increases with network size. We show that this in practice implies that large and sparse networks will require any integral control to be centralized, rather than distributed. In this case, the best-achievable performance scaling, which is shown to be that of proportional feedback control, is retrieved.
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10:55-11:20, Paper FrB4.2 | |
>Optimal Denial-Of-Service Attack Sequence with Energy Constraint Over Lossy Networks |
Li, Menglin | Univ. of Science and Tech. of China |
Qin, Jiahu | Univ. of Science and Tech. of China |
Keywords: Networked Control Systems, Linear Systems
Abstract: A novel method is proposed for solving the optimal Denial-of-Service (DoS) attack scheduling problem against remote state estimation with energy constraint over the lossy network. The optimal attack scheduling sequence that maximizes the average expected estimation error over lossy networks is derived. Details of the technique are outlined.
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11:20-11:45, Paper FrB4.3 | |
>Linear Quadratic Optimal Control of Jump System Over Multiple Erasure Channels |
Mazumdar, Abhijit | Indian Inst. of Tech. Guwahati |
Krishnaswamy, Srinivasan | IIT Guwahati |
Majhi, Somanath | Indian Inst. of Tech. Guwahati |
Keywords: Networked Control Systems
Abstract: This paper considers the design of linear quadratic optimal controller for Markovian jump linear systems (MJLSs) over multiple lossy communication channels with correlated packet loss. Considering the Gilbert-Elliott channel model which takes into account the temporal correlation of the data packet losses, the finite horizon controller and the infinite horizon controller are designed under TCP-like protocol. Existence of the infinite horizon controller is investigated by analyzing convergence of the cost function. Further, we derive the finite horizon and the infinite horizon controller for a linear time invariant (LTI) system as a special case. Finally, for the infinite horizon case, we demonstrate the dependence of the convergence of the optimal cost on the control packet arrival probability.
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11:45-12:10, Paper FrB4.4 | |
>Distributed Obstacle Avoidance-Formation Control of Mobile Robotic Network with Coordinated Group Stabilization |
Chan, Nelson P.K. | Univ. of Groningen |
Jayawardhana, Bayu | Univ. of Groningen |
Scherpen, Jacquelien M.A. | Fac. Science and Engineering, Univ. of Groningen |
Keywords: Networked Control Systems, Robotics, Stability
Abstract: We present a distributed control law for a group of agents that solves the problem of formation control with obstacle avoidance and that can be combined with a coordinated group stabilization control law. In particular, we consider a control law that is given by a linear combination of distributed formation, distributed obstacle avoidance and centralized group motion control laws. Simulation results show the effectiveness of our proposed control law.
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12:10-12:35, Paper FrB4.5 | |
>Weak Consensus with Discrete-Valued Input and the Performance Dependency on Its Network Topology |
Morita, Ryosuke | Gifu Univ |
Ito, Satoshi | Gifu Univ |
Keywords: Networked Control Systems
Abstract: This paper presents a new consensus algorithm for multi-agent systems with discrete-valued input. The algorithm is designed with consideration that the convergence speed does not degrade. The relation between the performance of the algorithm and the network topology of the system is analyzed.
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12:35-13:00, Paper FrB4.6 | |
>Exponential Synchronization of Lohe Oscillators with Strongly Connected Topologies |
Zhang, Jinxing | Nanjing Normal Univ |
Zhu, Jiandong | School of Mathematical Sciences, Nanjing Normal Univ |
Keywords: Networked Control Systems, Systems on Graphs
Abstract: Lohe model is a typical dynamic network of nonlinear multi-agent systems. Under strongly connected topologies, the synchronization problem of Lohe oscillators is investigated. The obtained results show that, limited on a half unit sphere, synchronization of Lohe model can be achieved. To analyze exponential synchronization, a matrix Riccati differential equation of synchronization errors is proposed for the first time. It is proved that, after a finite amount of time, the synchronization errors converge to zero exponentially.
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FrB5 |
Room 2503 |
Nonlinear Systems and Control II |
Regular Session |
Chair: Mironchenko, Andrii | Univ. of Passau |
Co-Chair: Qian, Chunjiang | Univ. of Texas at San Antonio |
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10:30-10:55, Paper FrB5.1 | |
>Integral Uniform Global Asymptotic Stability and Non-Coercive Lyapunov Functions |
Mironchenko, Andrii | Univ. of Passau |
Wirth, Fabian R. | Univ. of Passau |
Keywords: Stability, Nonlinear Systems and Control, Infinite Dimensional Systems Theory
Abstract: In this paper, a class of abstract dynamical systems is considered which encompasses a wide range of nonlinear finite- and infinite-dimensional systems. We show that the existence of a non-coercive Lyapunov function without any further requirements on the flow of the forward complete system ensures an integral version of uniform global asymptotic stability. We prove that also the converse statement holds without any further requirements on regularity of the system. Furthermore, we give a characterization of uniform global asymptotic stability in terms of the integral stability properties and analyze which stability properties can be ensured by the existence of a non-coercive Lyapunov function, provided either the flow has a kind of uniform continuity near the equilibrium or the system is robustly forward complete.
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10:55-11:20, Paper FrB5.2 | |
>Asymptotic Stability of a Class of Nonlinear Systems Admitting Homogeneity with Strictly Decreasing Degrees |
Zhu, Jiandong | School of Mathematical Sciences, Nanjing Normal Univ |
Qian, Chunjiang | Univ. of Texas at San Antonio |
Keywords: Stability, Nonlinear Systems and Control
Abstract: Asymptotic stability is investigated for a class of inherently nonlinear systems admitting homogeneity with strictly decreasing degrees (HSDD). By using the technique of homogeneous domination and the concept of HSDD, a concrete Lyapunov/Chetaev function is constructively obtained. Then, by Lyapunov Stability Theorem and Chetaev Instability Theorem, a necessary and sufficient condition for the asymptotic stability is proposed. Finally, simulations are given to validate the theoretical result.
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11:20-11:45, Paper FrB5.3 | |
>Distributed Recursive Filter for Systems with Multiplicative Noises |
He, Xingkang | Acad. of Maths and Systems Sci, Chinese Acad. of Sciences |
Qian, Liu | The Key Lab. of Systems and Control, Inst. of Systems S |
Fang, Haitao | Acad. of Mathematics and Systems Science, Chinese Acad. Of |
Keywords: Signal Processing, Nonlinear Filtering and Estimation, Stability
Abstract: This paper studies the distributed state estimation problem for a class of linear time-invariant (LTI) systems with multiplicative noises over multi-agent networks. First, adaptive fusion matrices with distributed strategy is considered in terms of consistency, which provides an upper bound for mean square error matrix of each agent and the bound is minimized by the designed time-varying filter gain. Based on the designed fusion matrices and filter gain, a distributed robust Kalman filter is proposed. Moreover, under mild conditions of collective observability and network topology, it is shown that the mean square error matrices of agents are uniformly upper bounded and the information matrix of the network are uniformly lower bounded by constant matrices both through finite time, which is revealed to be the summation of collective observability parameter and network scale. Finally, the asymptotic unbiasedness of the estimation of each agent is shown. Numerical simulation shows the effectiveness of the proposed algorithm.
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11:45-12:10, Paper FrB5.4 | |
>A Mathematics Approach to Improve the Computational Efficiency of Economic-Oriented Model Predictive Control |
Fang, Yizhou | The Pennsylvania State Univ |
Armaou, Antonios | The Pennsylvania State Univ |
Keywords: Nonlinear Systems and Control, Optimal Control, Process Control
Abstract: In this paper, we propose a mathematics approach to improve the computational efficiency of economic-oriented model predictive control (EMPC). We approximate the nonlinear dynamic system with a Two-tier method: 1) Approximate the system through Taylor expansion and obtain a polynomial formulation; 2) Expand the polynomial formulation through Carleman approximation (also known as Carleman linearization) and arrive at an extended bilinear expression. This expression has a bilinear form but carries information of higher order dynamics. In this way, we save simulation efforts by predicting the future economic performances with analytical solutions. We also save optimization efforts by providing the sensitivity of the economic performances to the manipulated inputs as the search gradient. Hence, despite the economic stage costs are mostly non-tracking and non-quadratic, we achieve significant acceleration in the computation of EMPC. An oxidation of ethylene reactor is demonstrated as the application example. We optimize three manipulated inputs and establish a non-tracking cyclic operation. The improvement in computational efficiency is presented by comparison with standard EMPC method.
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12:10-12:35, Paper FrB5.5 | |
>Study on Stability of General Discrete-Time Stochastic Difference Systems |
Jiang, Xiushan | South China Univ. of Tech |
Zhang, Tianliang | South China Univ. of Tech |
Zhang, Weihai | Shandong Univ. of Sci. and Tech |
Keywords: Stability, Nonlinear Systems and Control, Stochastic Modeling and Stochastic Systems Theory
Abstract: In order to improve the previous results and obtain efficient criteria for discrete stochastic stability, new techniques should be introduced. In this paper, by using Doob's martingale theory and stopping time theorem for supermartingale, we have successfully generalized some classical stability theorems existing in It^o systems to general discrete stochastic system, which are expected to be useful in stochastic H_infty control and network control.
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12:35-13:00, Paper FrB5.6 | |
>Dynamic Output Feedback Invariants of Full Relative Degree Nonlinear SISO Systems |
Gray, W. Steven | Old Dominion Univ |
Duffaut Espinosa, Luis Augusto | Univ. of Vermont |
Keywords: Nonlinear Systems and Control, Algebraic Systems Theory, Applications of Algebraic and Differential Geometry in Systems Theory
Abstract: The goal of this paper is to explicitly describe invariants of a plant described by a Chen--Fliess series under a class of dynamic output feedback laws using earlier work by the authors on feedback transformation groups. The main result requires the rather strong assumption that the plant has a generating series with both finite Lie rank and full relative degree. In which case, there is no loss of generality in working with state space realizations of the plant. An additional genericness assumption regarding the normal form of the plant is also required, but as shown by the examples, this condition is often available in typical problems. All of the analysis presented is restricted to the single-input, single-output case.
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FrB6 |
Room 2504 |
Systems on Graphs |
Regular Session |
Chair: Caines, Peter E. | McGill Univ |
Co-Chair: Liu, Cheng-Lin | Jiangnan Univ |
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10:30-10:55, Paper FrB6.1 | |
>Consensus-Induced Centrality for Networks of Dynamical Systems |
Gao, Shuang | McGill Univ |
Caines, Peter E. | McGill Univ |
Keywords: Systems on Graphs, Mathematical Theory of Networks and Circuits, Algebraic Systems Theory
Abstract: In multi-agent systems where agents are coupled through the underlying networks and follow the consensus dynamics, the ability for agents on networks to reach consensus depends on the network structure, and more specifically depends on the spectra of the Laplacian of the networks. Each agent on the network plays a role in aggregating the information for the agent population to reach a consensus. To evaluate the influence that one agent would have on the network to reach consensus, we propose the consensus-induced centrality measure. Examples of consensus-induced centrality analysis for different types of networks are given. The consensus-induced centrality has possible applications in many network systems, such as social networks, power grid stability and wireless sensor networks, etc.
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10:55-11:20, Paper FrB6.2 | |
>Mixing Rates for the Cycle with Structured Additional Wiring |
Gerencser, Balazs | MTA Alfréd Rényi Inst. of Mathematics, ELTE Eötvös Loránd Un |
Hendrickx, Julien M. | UCL |
Keywords: Systems on Graphs, Communication Systems
Abstract: We analyze the mixing rate of a class of Markov chains where two features together help significantly speed up mixing: first, a cycle graph is enriched with extra edges in a randomized but structured way. Second, the Markov chain on the graph is taken to be asymmetric. We show a bound on the mixing rate of these Markov chains and demonstrate that both these features contribute to the outcome.
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11:20-11:45, Paper FrB6.3 | |
>Persistent-Hold Consensus Control of First-Order Multi-Agent Systems with Intermittent Communication |
Liu, Cheng-Lin | Jiangnan Univ |
Zhang, Ya | Southeast Univ |
Chen, Yangyang | Southeast Univ |
Keywords: Systems on Graphs, Networked Control Systems, Robotics
Abstract: Under intermittent communication, a persistent-hold consensus algorithm is proposed to solve the consensus problem of first-order multi-agent systems. Based on matrix theory and graph theory, consensus conditions are obtained for the agents converging to the asymptotic consensus under fixed topology and switching topologies, respectively. Numerical simulations show the correctness of theoretical results.
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11:45-12:10, Paper FrB6.4 | |
>A Scheme for Computing the Transfer Function of Power Grids with Grounded Capacitors |
Jeeninga, Mark | Univ. of Groningen |
De Persis, Claudio | Univ. of Groningen |
van der Schaft, Arjan J. | Univ. of Groningen |
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12:10-12:35, Paper FrB6.5 | |
>Further Study on Parameter Bound of Surplus-Based Averaging Algorithm |
Kawamura, Satoshi | Osaka City Univ |
Cai, Kai | Osaka City Univ |
Ye, Mengbin | Australian National Univ |
Keywords: Networked Control Systems, Systems on Graphs, Mathematical Theory of Networks and Circuits
Abstract: We study a continuous-time surplus-based algorithm for multi-agent average consensus, and derive a tight upper bound on the key parameter included in this algorithm that ensures convergence over strongly connected and balanced digraphs. Based on this result, it is suggested through extensive simulation that, for the same number of agents, the upper bound for cyclic digraphs be smaller than that for other strongly connected and possibly unbalanced digraphs; this implies that as long as the parameter satisfies the upper bound for cyclic digraphs, this parameter can work for other digraphs.
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12:35-13:00, Paper FrB6.6 | |
>Strong Input-To-State Stability for Infinite Dimensional Linear Systems (I) |
Nabiullin, Robert | Univ. of Wuppertal |
Schwenninger, Felix Leopold | Univ. of Hamburg |
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FrB7 |
Room 5506 |
Advances in Multi-Agent Systems |
Invited Session |
Chair: Wang, Xinghu | Univ. of Science and Tech. of China |
Organizer: Wang, Xinghu | Univ. of Science and Tech. of China |
Organizer: Zeng, Xianlin | Beijing Inst. of Tech |
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10:30-10:55, Paper FrB7.1 | |
>Distributed Nash Equilibrium Seeking for Non-Cooperative Games Subject to Coupled Inequality Constraints: A Time-Scale Separation Approach (I) |
Zou, Yao | Tsinghua Univ |
Huang, Bomin | Tsinghua Univ |
Meng, Ziyang | Tsinghua Univ |
Keywords: Optimization : Theory and Algorithms, Networked Control Systems, Large Scale Systems
Abstract: This paper investigates the Nash equilibrium seeking problem for non-cooperative games subject to a coupled inequality constraint. Both the local cost functions and the constrained function are mutually coupled by the decision variables of players. A distributed seeking algorithm is proposed via local information interaction. First, a distributed observer with the projection property is introduced for each player to estimate the decision variables of all the other players. By using these estimations, a seeking algorithm with the projection property is then synthesized. The stability analysis is based on a time-scale separation approach. In particular, we first show that the fast dynamics composed by the distributed observer with an appropriate parameter guarantees that the estimation errors converge to an arbitrarily small neighborhood of the origin in finite time and maintain within it afterwards. Based on this result, we further show that the slow dynamics composed by the seeking algorithm achieves the convergence of the strategy profile to a neighborhood of the generalized Nash equilibrium of interest. an illustrative example is provided to verify the theoretical results.
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10:55-11:20, Paper FrB7.2 | |
>Robust H-Infinity Time-Varying Formation Tracking for High-Order Multi-Agent Systems with External Disturbances (I) |
Yu, Jianglong | Beihang Univ |
Dong, Xiwang | Beihang Univ |
Liang, Zixuan | Beihang Univ |
Li, Qingdong | Beihang Univ |
Ren, Zhang | Beihang Univ |
Keywords: Robust and H-Infinity Control, Nonlinear Systems and Control, Large Scale Systems
Abstract: Robust H-infinity time-varying formation tracking problems for high-order multi-agent systems with matched and mismatched disturbances under directed topologies are investigated. In this paper, the followers are required to form a formation specified by a time-varying piecewise continuously differentiable vector while tracking the trajectory of the leader containing unknown control input with a H1 disturbance attenuation performance. Firstly, a distributed formation tracking protocol is put forward which is constituted by using local neighboring information. An approach to designing the protocol for high-order multi-agent systems to achieve the robust H-infinity time-varying formation tracking is proposed, where the formation tracking feasibility constraint is also derived. Stability of the closed-loop multi-agent system under the protocol is proved. Finally, the effectiveness of the theoretical results are verified by a third-order simulation example.
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11:20-11:45, Paper FrB7.3 | |
>Smooth Algorithm for Nonsmooth Convex Optimization Using Proximal Operator and Derivative Feedback (I) |
Zeng, Xianlin | Beijing Inst. of Tech |
Chen, Jie | Beijing Inst. of Tech |
Keywords: Optimization : Theory and Algorithms, Stability, Large Scale Systems
Abstract: This paper considers a class of nonsmooth convex optimization problems whose objective function is the summation of a twice differentiable convex function and a lower semi-continuous convex function. Using the proximal operator and derivative feedback ideas, we propose a smooth algorithm for the problem and prove the convergence and correctness of the algorithm. The design is then applied to distributed optimization problems
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11:45-12:10, Paper FrB7.4 | |
>Finite-Time Coordination Control for a Class of Second-Order Nonlinear Multi-Agent Systems (I) |
Li, Zhenxing | Southeast Univ |
Liu, Zhaodong | Linyi Univ |
Guochen, Pang | Linyi Univ |
Keywords: Networked Control Systems, Nonlinear Systems and Control
Abstract: In this paper, we consider the distributed finite-time consensus control for a class of second-order nonlinear multi-agent systems. In order to design the finite-time consensus controller, homogeneous function was employed and a new type of distributed finite-time consensus controller was given. This kind of controller not only solves the finite-time consensus problem of leaderless second-order nonlinear multi-agent systems, but also relaxes the condition of the network topology among the agents from undirected graph or detail-balanced directed graph to strongly connected graph. In the real control engineering, the most common sensors are displacement sensor and acceleration sensor, the velocity information is not available directly. When velocity information is not available, the finite-time convergent observer is designed by using position information, and we give another kind of finite-time consensus controller for multi-agent systems based on the states of the finite-time observers.
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12:10-12:35, Paper FrB7.5 | |
>Distributed Optimization for Multi-Agent Systems of Independent Step Size (I) |
Wang, Dong | Dalian Univ. of Tech |
Chen, Yangwei | Dalian Univ. of Tech |
Keywords: Networked Control Systems, Optimization : Theory and Algorithms
Abstract: In this paper, we develop a distributed algorithm for multiple agents aiming to solve an optimization problem. The communication among the agents is governed by an undirected graph. In our algorithm, each agent uses an independent step-size and the upper bound of steps are independent from network topologies. The step-sizes depend on local objective functions. We present an algorithm that even with different step sizes guarantees convergence of the agent states to a common point.With such step range, the states of each agent converge to a common optimal point at a linear rate O({kappa ^{ - k}}) where 0
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12:35-13:00, Paper FrB7.6 | |
>Robust Distributed Control of Uncertain Nonlinear Vehicle Platoons (I) |
Zhong, Bin | USTC |
Wang, Xinghu | Univ. of Science and Tech. of China |
Keywords: Networked Control Systems, Nonlinear Systems and Control, Robust and H-Infinity Control
Abstract: This paper studies the distributed control problem of uncertain vehicle platoons. The vehicle is modelled by a third-order nonlinear longitudinal dynamics. Under general directed information flow topologies, we propose a robust distributed controller embedding adaptive laws to estimate the control gains. By using the Lyapunov method, we show that the developed control law can ensure that all the uncertain nonlinear vehicles in question track a desired speed and maintain a fixed inter-vehicle spacing.
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FrD1 |
Room 2463 |
Analysis and Control of Networked and Large-Scale Systems |
Invited Session |
Chair: Cai, Kai | Osaka City Univ |
Co-Chair: Vargas, Francisco J. | Univ. Técnica Federico Santa María |
Organizer: Chen, Wei | The Hong Kong Uni. of Sci. and Tech |
Organizer: Qiu, Li | Hong Kong Univ. of Sci. & Tech |
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16:00-16:25, Paper FrD1.1 | |
>Opinion Dynamics with State-Dependent Susceptibility to Influence (I) |
Ye, Mengbin | Australian National Univ |
Liu, Ji | Stony Brook Univ |
Anderson, Brian D.O. | Australian National Univ |
Keywords: Networked Control Systems, Large Scale Systems, Nonlinear Systems and Control
Abstract: A general discrete-time opinion dynamics model is studied in this paper. It is proposed that each individual has a susceptibility to being influenced by his/her neighbours, and that this susceptibility depends on the individual's current opinion value. This precept is captured by a state-dependent susceptibility function. Two different susceptibility functions are proposed to describe individuals who are stubborn conformists and stubborn extremists. Stubborn conformists are individuals who become more closed to influence when they have an opinion similar to the network average, while stubborn extremists are less susceptible when they hold opinions at either end of the opinion interval. Convergence results are established for networks where all individuals are stubborn conformists, or all individuals are stubborn extremists. Simulations are provided to illustrate the results. Key conclusions, consistent with sociology literature and exemplified by the simulations are that (i) stubborn conformists typify observed phenomenon whereby it takes a long time for people to agree on social norms, and an equally difficult time breaking them, and (ii) existence of stubborn extremists can pull individuals with an initial neutral opinion to the extremes.
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16:25-16:50, Paper FrD1.2 | |
>Fundamental Limitations of Feedback and Networked Feedback Systems: An Information-Theoretic Analysis (I) |
Fang, Song | City Univ. of Hong Kong |
Chen, Jie | City Univ. of Hong Kong |
Ishii, Hideaki | Tokyo Inst. of Tech |
Keywords: Networked Control Systems, Information Theory, Stochastic Control and Estimation
Abstract: In this extended abstract we analyze the fundamental performance limitations of feedback and networked feedback systems by leveraging information-theoretic notions including entropy and mutual information, as an attempt towards bridging control theory and information theory. In particular, we develop Bode-type integrals, power gain bounds, and variance minimization limits applicable to information-constrained networked feedback systems, which hold for arbitrarily general controllers as long as they are causal and stabilizing. Towards this end, we propose a number of information measures such as negentropy rate, channel blurredness, and Gaussianity-whiteness compatible to control system analysis. We also investigate feedback systems without communication channels; in particular, we examine the results further in the context of state estimation. In general, the performance limitations are seen to be characterized by plant instabilities, channel noisiness, and disturbance Gaussianity-whiteness. In summary, this abstract presents a unifying information-theoretic framework for control system limitation analysis, and consolidates the role of Shannon's information theory as a mathematical theory of not only communication but also control.
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16:50-17:15, Paper FrD1.3 | |
>On Spectral Properties of Directed Scale-Free Networks (I) |
Imae, Takanobu | Osaka City Univ |
Cai, Kai | Osaka City Univ |
Keywords: Large Scale Systems, Systems on Graphs, Networked Control Systems
Abstract: In this paper, we study the spectral properties of directed scale-free networks. First, we study the algebraic connectivity of a directed scale-free network, which is the eigenvalue of its Laplacian matrix whose real part is the second smallest. This is known as an important measure for the diffusion speed of many diffusion processes over networks (e.g. consensus, information spreading, epidemics). We also investigate the eigenvalue of the Laplacian matrix with maximum real part. We propose an algorithm, extending that of Barabasi and Albert, to generate directed scale-free networks, and show by simulations the relations between the spectral properties and network size, exponents of in/out-degree distributions, and minimum in/out degrees.
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17:15-17:40, Paper FrD1.4 | |
>Dynamics of Heterogeneous Mass Chains Via Repeated Compositions of Moebius Transformations (I) |
Yamamoto, Kaoru | Lund Univ |
Keywords: Networked Control Systems, Large Scale Systems, Mechanical Systems
Abstract: This note studies the disturbance amplification in an interconnected heterogeneous mass chain in which one end is connected to a movable point. Each interconnection is represented by a general mechanical impedance function. The problem arises in the design of multi-storey buildings subjected to earthquake disturbances, or bidirectional control of vehicle platoons. Recurrence relations with respect to the number of masses are derived for the scalar transfer functions from the movable point displacement to a given intermass displacement. In particular, each relation takes the form of a Moebius transformation.
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17:40-18:05, Paper FrD1.5 | |
>String Stability for Predecessor Following Platooning Over Lossy Communication Channels (I) |
Vargas, Francisco J. | Univ. Técnica Federico Santa María |
Maass, Alejandro I. | The Univ. of Melbourne |
Peters, Andres | Univ. Técnica Federico Santa María |
Keywords: Stability, Networked Control Systems, Large Scale Systems
Abstract: We study a platooning scheme where the communication between agents is made through lossy channels. Each agent is modelled as a discrete-time LTI system controlled by a discrete-time LTI controller. The lossy channels are modelled using Bernoulli processes that represent random data dropouts. We consider a scheme that forces inter-vehicle spacings that increase with agents velocities. This is known as a constant time headway spacing policy, which has been shown to provide string stability for predecessor-following architectures. We analyse how the lossy channels impact the platoon string stability.
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FrD2 |
Room 2464 |
Linear Systems |
Regular Session |
Chair: Ohta, Yoshito | Kyoto Univ |
Co-Chair: Phan, Duy | Tampere Univ. of Tech |
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16:00-16:25, Paper FrD2.1 | |
>Distributed Fault Detection Observer Design for Linear Systems |
Han, Weixin | Harbin Inst. of Tech |
Trentelman, Harry L. | Univ. of Groningen |
Wang, Zhenhua | Harbin Inst. of Tech |
Shen, Yi | Harbin Inst. of Tech |
Keywords: Linear Systems, Networked Control Systems
Abstract: This paper investigates the distributed fault detection problem for linear time-invariant (LTI) systems with distributed measurement output. We propose a distributed fault detection observer (DFDO) design method to detect actuator faults of the monitored system in the presence of a bounded process disturbance. The DFDO consists of a network of local fault detection observers, which communicate with their neighbors as prescribed by the given network graph. A systematic algorithm for DFEO design is addressed, enabling the residual to be robust against the effects of the external bounded process disturbance. Based on L_{infty} analysis, a bank of linear matrix inequalities is presented to calculate the gain matrices and residual thresholds in our distributed fault detection scheme. Finally, we illustrate the effectiveness of the proposed distributed fault detection approach by means of a numerical simulation.
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16:25-16:50, Paper FrD2.2 | |
>System Transformation Induced by Generalized Orthonormal Basis Functions Preserves Dissipativity |
Ohta, Yoshito | Kyoto Univ |
Rapisarda, Paolo | Univ. of Southampton |
Keywords: Linear Systems, Robust and H-Infinity Control
Abstract: This paper discusses the dissipativity of transformed systems induced by generalized orthonormal basis functions. The dissipativity includes both passivity and the finite system gain property. We prove that the transformed system preserves the dissipativity and shares a common storage function when the original continuous-time system is dissipative. The results further illuminates the properties of this class of system transformation.
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16:50-17:15, Paper FrD2.3 | |
>Model Reduction of Linear Port-Hamiltonian Systems: A Structure Preserving Approach |
Borja, Pablo | Univ. of Groningen |
Scherpen, Jacquelien M.A. | Fac. Science and Engineering, Univ. of Groningen |
Keywords: Linear Systems
Abstract: In this note we address the problem of model reduction of a particular class of linear systems, namely, the linear port-Hamiltonian (PH) systems. Furthermore, we explore the preservation of the PH structure in the reduced model. Towards this end, we adopt the balanced truncation approach to reduced the order of the model, in particular, we study the use of extended Gramians to balance the linear PH systems. The latter provides degrees of freedom to impose a desired structure, in this case a PH one, to the reduced model. Moreover, for balanced truncation using extended Gramians, the error bound is well-known and is given in terms of the Hankel singular values of the truncated state.
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17:15-17:40, Paper FrD2.4 | |
>Robust Controllers for a Heat Equation Using the Galerkin Approximation |
Phan, Duy | Tampere Univ. of Tech |
Paunonen, Lassi | Tampere Univ. of Tech |
Keywords: Robust and H-Infinity Control, Feedback Control Systems, Linear Systems
Abstract: We consider the robust output tracking problem for an unstable one-dimensional heat equation. As the main contribution we propose a new way of designing finite-dimensional robust controllers based on Galerkin approximations of infinite-dimensional observer-based controllers. The results are illustrated with a concrete example where the finite-dimensional controllers are constructed using the Finite Element Method. The results are extendable for more general parabolic control systems.
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17:40-18:05, Paper FrD2.5 | |
>Toward a Decay Rate Assignment Based Design for Time-Delay Systems with Multiple Spectral Values |
Boussaada, Islam | IPSA & Lab. Des Signaux Et Systèmes |
Niculescu, Silviu-Iulian | Umr Cnrs 8506, Cnrs-Supelec |
Trabelsi, Karim | IPSA |
Keywords: Delay Systems, Linear Systems, Stability
Abstract: Recent results on maximal multiplicity induced-dominancy for spectral values in reduced-order Time-Delay Systems naturally apply in controllers design. As a matter of fact, the approach is merely a delayed-output-feedback where the candidates’ delays and gains result from the manifold defining the maximal multiplicity of a real spectral value, then, the dominancy is shown using the argument principle. Various reduced order examples illustrate the applicative perspectives of the approach.
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FrD3 |
Room 2465 |
Signal Processing |
Regular Session |
Chair: Rao, Shodhan | Ghent Univ. Global Campus |
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16:00-16:25, Paper FrD3.1 | |
>Sparse Regression Using Compressive Sensing with Input Shaping |
Borkar, Vivek S. | Indian Inst. of Tech. Bombay |
Dwaracherla, Vikranth | IIT Bombay |
Sahasrabudhe, Neeraja | IISER Mohali |
Keywords: Signal Processing
Abstract: We present a compressive sensing approach for sparse regression problem and using the ideas from concentration of measure, extend it to case where the samples are generated from a Markov chain. This is achieved by constructing a matrix from samples such that it is suitable for reconstructing sparse parameter vectors via l_1-minimization.
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16:25-16:50, Paper FrD3.2 | |
>Lyapunov Functions for Michaelis Menten Approximation of Processive Phosphorylation Futile Cycles |
Rao, Shodhan | Ghent Univ. Global Campus |
Keywords: Systems Biology, Stability, Biological Systems
Abstract: In this paper, we analyze a class of processive phosphorylation futile cycles in which a given protein substrate is modified by more than two enzymes. This analysis is based on the assumption that the initial concentration of the protein substrate is much higher than the concentrations of the enzymes. This assumption allows us to reduce the dynamics of the system to its Michaelis Menten approximation using the steady state approach. We then prove that for the given system of equations, there exists a unique equilibrium concentration vector in every positive stoichiometric compatibility class. We further prove that this unique equilibrium is globally asymptotically stable using two different Lyapunov functions. The first Lyapunov function is a piecewise linear in rates (PWLR) Lyapunov function. The construction of the second Lyapunov function is based on the property of strict convexity of the exponential function.
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16:50-17:15, Paper FrD3.3 | |
>A New Symmetric Key Homomorphic Encryption Scheme |
Dowerah, Uddipana | Indian Inst. of Tech. Guwahati |
Krishnaswamy, Srinivasan | IIT Guwahati |
Keywords: Information Theory, Communication Systems, Coding Theory
Abstract: This work describes a new Symmetric Key Homomorphic Encryption scheme. We define a noisy variant of the Subspace Membership problem called the Hidden Subspace Membership problem and show that the proposed scheme is IND-CPA secure based on the hardness of this problem. We then discuss the homomorphic properties of the proposed scheme.
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17:15-17:40, Paper FrD3.4 | |
>On the Uniqueness of Maximum Likelihood Estimation of Nuclear Sources |
Haug, Josh | Univ. of Iowa |
Anjum, Mohammad Fahim | Univ. of Iowa |
Anderson, Brian D.O. | Australian National Univ |
Dasgupta, Soura | Univ. of Iowa |
Mudumbai, Raghuraman | Univ. of Iowa |
Baidoo-Williams, Henry | Univ. of Iowa |
Keywords: Feedback Control Systems, Signal Processing, Stability
Abstract: In an earlier paper, cite{ITA}, we have considered the Maximum Likelihood (ML) localization of a stationary nuclear source using the time of arrival of particles modeled as a Poisson process. In this paper we consider whether the ML location estimate characterized in cite{ITA} is unique. In particular, we show that the question of uniqueness is equivalent to whether or not the root locus of a certain transfer function admits a single pair of nonzero imaginary axis crossing.
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FrD4 |
Room 2502 |
Networked Control Systems III |
Regular Session |
Chair: Petersen, Ian R. | Australian National Univ |
Co-Chair: Li, Yuke | Yale Univ |
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16:00-16:25, Paper FrD4.1 | |
>The Power Allocation Game on a Dynamic Network: Equilibrium Selection |
Li, Yuke | Yale Univ |
Morse, A. Stephen | Yale Univ |
Keywords: Mathematical Theory of Networks and Circuits, Optimization : Theory and Algorithms, Systems on Graphs
Abstract: This note proposes two equilibrium selection methods and applies them to the power allocation game developed in cite{allocation}. The first method has the game take place on a sequence of time-varying graphs, which redefines the PAG in an extensive form game framework, and selects the subgame perfect Nash equilibria. The second method has the power allocation game take place on a different sequence of time-varying graphs and selects the ``resilient'' Nash equilibria, where the concept of ``resilience'' is taken from the literature of network security. Certain technical results as well as the link between the two methods will be discussed. Either method is also applicable to equilibrium selection problems involving other network games.
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16:25-16:50, Paper FrD4.2 | |
>Spatio-Temporal Transfer Function Conditions of Positive Realness for Translation Invariant Lattice Networks of Interacting Linear Systems |
Vladimirov, Igor G. | Australian National Univ |
Petersen, Ian R. | Australian National Univ |
Keywords: Mathematical Theory of Networks and Circuits, Infinite Dimensional Systems Theory, Operator Theoretic Methods in Systems Theory
Abstract: This paper is concerned with networks of interacting linear systems at sites of a multidimensional lattice. The systems are governed by linear ODEs with constant coefficients driven by external inputs, and their internal dynamics and coupling with the other component systems are translation invariant. Such systems occur, for example, in finite-difference models of large-scale flexible structures manufactured from homogeneous materials. Using the spatio-temporal transfer function of this translation invariant network, we establish conditions for its positive realness in the sense of energy dissipation. The latter is formulated in terms of block Toeplitz bilinear forms of the input and output variables of the composite system. We also discuss quadratic stability of the network in isolation from the environment and phonon theoretic dispersion relations.
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16:50-17:15, Paper FrD4.3 | |
>On a Concept of Genericity for RLC Networks |
Hughes, Timothy H. | Univ. of Exeter |
Morelli, Alessandro | Univ. of Cambridge |
Smith, Malcolm C. | Univ. of Cambridge |
Keywords: Mathematical Theory of Networks and Circuits, Linear Systems, Algebraic Systems Theory
Abstract: A generic network is a resistor-inductor-capacitor (RLC) network which realises a set of impedance parameters of dimension one more than the number of elements in the network. We prove that such networks are minimal, in the sense that it is not possible to realise a set of impedance parameters of dimension n with fewer than n-1 elements. We provide a necessary and sufficient condition for genericity in terms of the derivative of the mapping from element values to impedance parameters. We then prove that a network with a non-generic subnetwork is itself non-generic, and that any positive-real impedance can be realized by a generic network.
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17:15-17:40, Paper FrD4.4 | |
>A Convex Approach to the Finite Dimensional Matching Problem in Communication Systems |
Bose, Gibin | INRIA Sophia Antipolis |
Martinez Martinez, David | INRIA Sophia Antipolis |
Seyfert, Fabien | INRIA |
Olivi, Martine | INRIA |
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17:40-18:05, Paper FrD4.5 | |
>Stochastic Mirror Descent Algorithm Over Distributed Time-Varying Network |
Wang, Yinghui | Chinese Acad. of Sciences and Univ. of Chinese Acad. Of |
Zhou, Hongbing | Acad. of Mathematics and Systems Science, Chinese Acad. of S |
Hong, Yiguang | Chinese Acad. of Sciences |
Keywords: Optimization : Theory and Algorithms
Abstract: In this paper, we propose a stochastic mirror descent algorithm for solving distributed convex optimization problem over a distributed time-varying network. We adopt Bregman divergence rather than Euclidean distance as the augmented distance measuring function to solve the distributed onvex optimization problem. With a fixed step-size, we analyze the convergence rate of our algorithm, which is also the best known convergence rate for distributed first-order algorithms.
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FrD5 |
Room 2503 |
Nonlinear Systems and Control III |
Regular Session |
Chair: Karlsson, Johan | Royal Inst. of Tech. (KTH) |
Co-Chair: Dia, Roxana | CEA-LETI |
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16:00-16:25, Paper FrD5.1 | |
>A Universal Model-Free and Safe Adaptive Cruise Control Mechanism |
Berger, Thomas | Univ. Hamburg |
Rauert, Anna-Lena | Univ. Hamburg |
Keywords: Adaptive Control, Nonlinear Systems and Control
Abstract: We consider the problem of vehicle following, where a safety distance to the leader vehicle is guaranteed at all times and a favourite velocity is reached as far as possible. We introduce the funnel cruise controller as a novel universal adaptive cruise control mechanism which is model-free and achieves the aforementioned control objectives. The controller consists of a velocity funnel controller, which directly regulates the velocity when the leader vehicle is far away, and a distance funnel controller, which regulates the distance to the leader vehicle when it is close so that the safety distance is never violated. A sketch of the feasibility proof is given. The funnel cruise controller is illustrated by a simulation of three different scenarios which may occur in daily traffic.
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16:25-16:50, Paper FrD5.2 | |
>Energy-Based Stabilization of Network Flows in Multi-Machine Power Systems |
Arghir, Catalin | ETH Zurich |
Dörfler, Florian | ETH Zürich |
Keywords: Nonlinear Systems and Control, Mathematical Theory of Networks and Circuits, Networked Control Systems
Abstract: This paper considers the network flow stabilization problem in power systems and adopts an output regulation viewpoint. Building upon the structure of a heterogeneous port-Hamiltonian model, we integrate network aspects and develop a systematic control design procedure. First, the passive output is selected to encode two objectives: consensus in angular velocity and constant excitation current. Second, the non-Euclidean nature of the angle variable reveals the geometry of a suitable target set, which is compact and attractive for the zero dynamics. On this set, circuit-theoretic aspects come into play, giving rise to a network potential function which relates the electrical circuit variables to the machine rotor angles. As it turns out, this energy function is convex in the edge variables, concave in the node variables and, most importantly, can be optimized via an intrinsic gradient flow, with its global minimum corresponding to angle synchronization. The third step consists of explicitly deriving the steady-state control action by further refining this sequence of control-invariant sets. Analogously to solving the so called regulator equations, we obtain an impedance-based network flow map leading to novel error coordinates and a shifted energy function. The final step amounts to decoupling the rotor current dynamics via feedback-linearziation resulting in a cascade which is used to construct an energy-based controller hierarchically.
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16:50-17:15, Paper FrD5.3 | |
>General Inverse Sensor Model for Probabilistic Occupancy Grid Maps Using Multi-Target Sensors |
Dia, Roxana | CEA-LETI |
Lesecq, Suzanne | CEA |
Mottin, Julien | CEA-LETI |
Puschini, Diego | CEA-Leti |
Keywords: Robotics
Abstract: Environment perception is a crucial task for safe navigation of robots. It relies on the robust interpretation of noisy sensor measurements. To represent the state of the surrounding environment, probabilistic Occupancy Grids are commonly used. They are built using a Bayesian inference procedure which estimates the occupancy probability of each cell in the grid from sensor readings. However, the complexity of such a procedure is exponentially increasing with the number of cells, especially when sensor readings are caused by multiple targets simultaneously. To overcome this difficulty, we propose a novel approach to handle multi-target sensors. It is based on a sectoral decomposition of their Field-Of-View under the nearest-target hypothesis, which breaks down the complexity to a linear one. Finally, a realistic implementation of the proposed formulation is presented, and an experimental construction of occupancy grids is discussed.
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17:15-17:40, Paper FrD5.4 | |
>Tracking Distributions of Linear Dynamical Systems: An Optimal Mass Transport Approach |
Chen, Yongxin | Univ. of Minnesota |
Karlsson, Johan | Royal Inst. of Tech. (KTH) |
Keywords: Nonlinear Filtering and Estimation, Stochastic Control and Estimation, Operator Theoretic Methods in Systems Theory
Abstract: We consider the problems of tracking a set of indistinguishable agents with linear dynamics based only on output measurements. The behaviors of the agents may be modeled by distributions. We formulate the problems using optimal mass transport theory with prior linear dynamics. Though our problem has a convex formulation, with general purpose solver, it is only computationally feasible if the state dimension is low. In the case where the marginal distributions are Gaussian, the problem is reformulated as a semidefinite programming and can be efficiently solved for large state dimension.
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17:40-18:05, Paper FrD5.5 | |
>Acceleration of Convergence While Tracking Planned Feature Trajectories for Visual Servoing |
Shen, Tiantian | Central South Univ |
Feng, Zhiguang | The Univ. of Hong Kong |
Keywords: Robotics, Optimization : Theory and Algorithms
Abstract: This extended abstract illustrates mainly an idea for accelerating the convergence in eye-in-hand visual servoing applications. Path-planning techniques have been embedded into VS (Visual Servoing) to guide the sensor motion satisfying multiple constraints and limitations. Ahead of visual servoing, path-planning techniques can produce a series of feature trajectories, either projected from a target when the camera virtually moves along the planned camera path or directly planned in the image plane. These feature trajectories are then interpolated and tracked by an IBVS (Imaged Based VS) controller to conduct a converged VS process. In general, larger the interpolation interval or the controller gain, quicker the convergence and, unfortunately, probably larger the tracking error of the planned path and even divergence in the workspace due to image noises. This abstract aims to obtain an optimal interpolation interval under a certain interpolation policy and an associated controller gain under an upper bound of tracking error defined in the workspace to accelerate the global convergence of path-planning based VS applications.
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