Keywords: Coding Theory
Abstract: We present a code-based cryptosystem, in which we use Reed-Solomon codes as secret codes and a weight two matrix for masking, to make the system secure against attacks based on the Schur product. We combine this with the Guruswami-Sudan list decoding for decryption to get lower key sizes. As a consequence, we obtain a key size reduction of 21.8% compared to the standard McEliece cryptosystem proposed by Bernstein et al.

Keywords: Coding Theory, Information Theory
Abstract: Securing information involves multiple layers: mathematical encryption, protocol design, software implementation and hardware implementation. Multiple disciplines are involved, mathematicians, software developers, telecommunication technicians and cybersecurity engineers.

Mathematical cryptanalysis analyses encrypted information, whereas side channel cryptanalysis analyses information leaked via software/hardware implementation. In this presentation we give an overview of reaction attacks due to protocol-based leaked information. We particularly look at McEliece Cryptosystems, also called Code Based Cryptography, using LDPC codes. The LDPC McEliece crypto system is vulnerable to reaction attacks.

We discuss reaction attacks that use decryption failure events to gather information about the decryption key. We propose to consider such decryption failures as a side channel from which information can be gathered. We conclude that any code-based cryptographic protocol requires careful cybersecurity engineering management of decryption failure events.

Keywords: Algebraic Systems Theory, Information Theory, Coding Theory
Abstract: Given a finite sequence of scalars, the Berlekamp-Massey algorithm solves the problem of finding a linear feedback shift register of minimal length which generates it. When instead of a sequence of scalars, we are given a sequence of matrices, it can be interpreted as the problem of finding a minimal partial realization and also as the problem of finding a minimal length right (left) matrix generator of the sequence. We generalize the main result standing the Berlekamp-Massey algorithm in terms of the partial Brunovsky indices of a finite sequence of matrices and design a strategy to obtain them. Once they are known, we can compute a minimal partial realization and a minimal length right (left) matrix generator of the sequence.

Keywords: Coding Theory
Abstract: In this paper we present a new variant of the McEliece cryptosystem. In contrast to the typical approach, where block codes are used, we propose the use of a convolutional encoder to be part of the public key. In this setting the message is a sequence of messages instead of a single block message and the errors are added randomly throughout the sequence. We point out several advantages of such an approach and indicate interesting lines for future research.

Keywords: Operator Theoretic Methods in Systems Theory, Multidimensional Systems, Robust and H-Infinity Control
Abstract: A natural partial ordering on self-adjoint matrices is to set A <= B whenever B - A is positive semidefinite. We say a function f:(a,b) -> R is matrix monotone in the sense that A <= B implies f(A) <= f(B), where f is evaluated using the functional calculus. (If the function f were a rational function, f(A) is simply defined by substituting A into f.) In 1934, Charles Loewner showed that a function is matrix monotone if and only if it is analytic and analytically continues to the upper half plane in C as a map into the closed upper half plane. With Ryan Tully-Doyle, we characterized the appropriate generalization for systems of matrix inequalities by proving a non-commutative version of Loewner’s theorem. Our work unites some of the basic theory already encountered in the wild in the study of matrix means, the Schur complement, random matrix theory, complete positivity, free probability and free analysis. In this talk, we will give the classical theory and some of its applications, then proceed to describe the notion of non-commutative function theory, and finally describe my current work on the non-commutative Loewner theorem with a several examples and applications.

Keywords: Linear Systems
Abstract: In "Foundations of Free Noncommutative Function Theory" Verbotvetskyi and Vinnikov introduce an algebraic construction that is used to develop a generalized derivative operator, called the difference-differential operator, for free noncommutative functions. This paper will construct an inverse to the difference-differential operator and determine what conditions must be imposed on an nc function to allow it to have an antiderivative.

Keywords: Operator Theoretic Methods in Systems Theory, Applications of Algebraic and Differential Geometry in Systems Theory
Abstract: A multivariate polynomial is stable if it has no zeros in the positive orthant of the C^n. Stable polynomials are a classical topic in control theory and in areas of mathematics ranging from complex analysis to real algebraic geometry. The talk describes a new class of results for noncommutative polynomials that attain only nonsingular values in the matricial positive orthant.

In recent years, there has been an increased interest in multivariate stable polynomials and closely related families (e.g. hyperbolic polynomials or rational inner functions). One of the most prominent new problems is the existence of distinguished determinantal representations for stable polynomials, which is related to the generalized Lax conjecture, the multivariate Pólya-Schur program, and the celebrated Kadison-Singer problem. Such a determinantal representation is a structural feature that naturally extends from scalar variables to matrix variables, which leads to questions about stable linear matrix pencils, and stable noncommutative polynomials and rational functions. The talk will address this noncommutative aspect of stability inspired by free analysis and free real algebraic geometry.

Keywords: Multidimensional Systems, Operator Theoretic Methods in Systems Theory
Abstract: The Beurling-Lax-Halmos theorem tells us that any invariant subspace {mathcal M} for the shift operator S colon f(z) mapsto z f(z) on the vectorial Hardy space over the unit disk H^{2}_{mathcal Y} = {f(z) = sum_{j=0}^{infty} f_{j} z^{j} colon | f |^{2} =sum_{j ge 0} | f_{j} |^{2} < infty} (the Reproducing Kernel Hilbert Space with reproducing kernel K(z,w) = (1 - z overline{w})^{-1} I_{mathcal Y}) can be represented as {mathcal M} = M_{Theta} H^{2}_{mathcal U} where M_{Theta} colon H^{2}_{mathcal U} to H^{2}_{mathcal Y} is an isometric multiplication operator M_{Theta} colon u(z) mapsto Theta(z) u(z). One proof constructs Theta as the transfer-function of a discrete-time input-state-output linear system explicitly constructed from the shift-invariant subspace cM. We discuss analogues of this result and related constructions for the setting of multivariable weighted Bergman spaces in the free noncommutative setting.

Keywords: Infinite Dimensional Systems Theory, Stochastic Modeling and Stochastic Systems Theory, Physical Systems Theory
Abstract: In this talk we focus on a particular instance of the realizability problem, namely, on the question of establishing whether two given functions non-negative and symmetric on the d-dimensional lattice (d positive integer) are the first two correlation functions of a translation invariant point process on on the d-dimensional lattice. We present a joint work with Emanuele Caglioti and Tobias Kuna, where we provide an explicit construction of such a process for any d>=2 under some natural assumptions relevant for applications in fluid theory and material science (iso-g processes).

Keywords: Optimal Control, Stability, Nonlinear Systems and Control
Abstract: This paper develops a curse-of-dimensionality-free numerical approach to construct control Lyapunov functions (CLFs) and stabilizing feedback strategies for deterministic control systems described by systems of ODEs. An extension of the Zubov method is used to represent a CLF as the value function for an appropriate infinite-horizon optimal control problem. The infinite-horizon stabilization problem is approximated by an exit time problem, with target set given by a sufficiently small closed neighborhood of the origin in the state space. In order to compute the related value function and optimal feedback control law separately at different initial states and thereby to attenuate the curse of dimensionality, an extension of a recently developed characteristics based framework is proposed. Theoretical foundations of the developed approach are given together with practical discussions regarding its implementation, and numerical examples are also provided. In particular, it is pointed out that the curse of complexity may remain a significant issue even if the curse of dimensionality is avoided.

Keywords: Optimal Control, Nonlinear Systems and Control, Computations in Systems Theory
Abstract: A standard max-plus eigenvector method arising in nonlinear optimal control is encapsulated within a basis function adaptation iteration. A level set corresponding to the target Hamiltonian back-substitution error is estimated at each step, using the value function approximation obtained by the eigenvector method. This estimate is used to construct and add new functions to the basis employed by the eigenvector method, with the objective of enlarging the target level set iteratively. The utility of the ensuing iteration is illustrated by example.

Keywords: Optimal Control, Optimization : Theory and Algorithms, Large Scale Systems
Abstract: This paper is about the computation of constrained optimal controls for series interconnections of heterogeneous sub-systems with linear discrete-time dynamics. The optimal control problem is first formulated in a form that is amenable to iterative solution by the alternating direction method of multipliers (ADMM). It is observed that this technique yields per-iteration computational burden that scales linearly in the both the number of systems along the cascade and the length of the time-horizon. Moreover, parallelization of the computation across a network of processors is possible with an information exchange architecture that mirrors the cascade structure of the system. Recent work, which also spatial structure within the context of interior point methods for the problem, achieves per-iteration computational cost that scales linearly in the cascade length, but cubically in the time horizon. On the other hand, interior point methods will typically take significantly fewer iterations to converge than the proposed first order method. With this in mind, convergence of the latter is explored numerically as the number of sub-systems and time horizon are varied.

Keywords: Optimal Control, Operator Theoretic Methods in Systems Theory
Abstract: We show that the joint spectral radius of a finite collection of nonnegative matrices can be bounded by the eigenvalue of a non-linear operator. This eigenvalue coincides with the ergodic constant of a risk-sensitive control problem, or of an entropy game, in which the state space consists of all switching sequences of a given length. We show that, by increasing this length, we arrive at a convergent approximation scheme to compute the joint spectral radius. The complexity of this method is exponential in the length of the switching sequences, but it is quite insensitive to the size of the matrices, allowing us to solve very large scale instances (several matrices in dimensions of order 1000 within a minute). An idea of this method is to replace a hierarchy of optimization problems, introduced by Ahmadi, Jungers, Parrilo and Roozbehani, by a hierarchy of nonlinear eigenproblems. We solve the latter problems by a power type iteration, avoiding the recourse to linear or semidefinite programming techniques, which allows for scalability. This is also related to maxplus-type curse of dimensionality attenuation schemes in dynamic programming.

Keywords: Nonlinear Systems and Control, Optimal Control, Physical Systems Theory
Abstract: Stationary-action problems for finite-dimensional conservative systems are considered. On sufficiently short time intervals, stationary-action trajectories typically correspond to least-action trajectories, and existence and uniqueness of these trajectories is easily demonstrated. However, for arbitrary duration problems, the stationary trajectory is not an optimizer, and in particular, there exist problem data where uniqueness does not hold. It is shown that, under certain conditions, points of non-uniqueness are isolated as a function of initial position. The conditions are verified in a classic two-body problem example. An extension of the implicit function theorem to certain cases where the usual first-order conditions are not satisfied is demonstrated and applied.

Keywords: Optimal Control, Optimization : Theory and Algorithms, Numerical and Symbolic
Abstract: In this talk we present a method for the a posteriori error estimation of the numerical solution to Hamilton-Jacobi-Bellman PDEs related to infinite horizon optimal control problems. The method uses the residual of the Hamiltonian, i.e., it checks how good the computed numerical solution satisfies the PDE and computes the difference between the numerical and the exact solution from this mismatch. We present results both for discounted and for undiscounted problems, which require different mathematical techniques. For discounted problems, an inherent contraction property can be used while for undiscounted problems an asymptotic stability property of the optimally controlled system is exploited.

Keywords: Networked Control Systems, Feedback Control Systems, Optimization : Theory and Algorithms
Abstract: We consider network routing under random link failures with a desired final distribution. We provide a mathematical formulation of a relaxed transport problem where the final distribution only needs to be close to the desired one. The problem is a maximum entropy problem for path distributions with an extra terminal cost. We show that the unique solution may be obtained solving a generalized Schroedinger system. An iterative algorithm to compute the solution is provided. It contracts the Hilbert metric with contraction ratio less than 1/2 leading to extremely fast convergence.

Keywords: Networked Control Systems, Optimization : Theory and Algorithms, Communication Systems
Abstract: In this paper, we consider a multiagent network system to solve a linear equation with quantized communication and distribution computation. We proposed a novel adaptive quantizer and an encoder-decoder design such that the linear equation could be solved by the agents with just quantized communication in a distributed manner.

Keywords: Networked Control Systems, Feedback Control Systems, Large Scale Systems
Abstract: We propose an anti-windup scheme for a class of control problems. This class, includes networked systems, where each node contains a subsystem and each edge comprise a control action. The networked anti-windup control system is proposed to address the issues caused by integrator state saturation. We show that the suggested control scheme is input-output stable. Furthermore, we provide a numerical method for robust performance analysis of the suggested control system.

Keywords: Networked Control Systems, Computer Networks, Stochastic Modeling and Stochastic Systems Theory
Abstract: We explore the networked control problem under the effects of disturbance and jamming attacks. Specifically, we consider the scenarios where an insecure wireless communication channel is used for transmission of the control input packets from the controller to the plant. This channel is assumed to face jamming attacks and the likelihood of transmission failures on this channel depends on the power of the jamming interference signal emitted by an attacker. We show that the combined effects of the jamming attacks and the disturbance can cause instability even if the attacked system without disturbance is stable. Furthermore, we show that stability under jamming and disturbance can be achieved if the average jamming interference power is restricted in a certain way.

Keywords: Networked Control Systems, Delay Systems, Linear Systems
Abstract: The paper studies the problem of the H2 (LQG) optimal control of LTI plants under irregular communication interruptions between the sensor- and actuator-side parts of the controller. The derived optimal solution is analytic, numerically simple, implementable, transparent, and requires no a priori information about the interruption intervals or their statistics. The result is generalized to incorporate a constant loop delay.

Keywords: Networked Control Systems
Abstract: This paper is concerned with challenges involved with implementation of a private observer in networked control systems. Here, a secure Luenberger observer over a network is considered. The Paillier encryption, which is a semi-homomorphic encryption method, is employed so that the algebraic calculations required for the estimation can be performed over the encrypted data. This enhances the security of the state estimation process. In particular, we study the challenges associated with implementation of such a private observer on digital processors with limited memory sizes. We provide conditions under which the stability of the implemented private observer is ensured. A numerical example is utilized to demonstrate the theoretical results.

Keywords: Physical Systems Theory, Nonlinear Systems and Control, Process Control
Abstract: In this work we expand on the symplectic formulation of thermodynamic systems exposed in our recent work, and inspired by previous work of Balian and Valentin. The main novel contribution is the geometric formulation of open thermodynamic systems as a homogeneous Lagrangian submanifold of the product of the symplectified thermodynamic phase space and a space of external variables. This leads to a natural property of shifted passivity to be used for analysis and control. Furthermore, it will be discussed how this homogeneous Lagrangian submanifold admits a natural (singular) Riemannian metric.

Keywords: Nonlinear Systems and Control, Applications of Algebraic and Differential Geometry in Systems Theory
Abstract: The notion of moment at a pole of a single-input, single-output, continuous-time, nonlinear, time-invariant system is studied. It is argued that the existing notion of moment at pole can be extended to wider classes of systems. The moment at a pole of a class of systems in feedback form is shown to be uniquely determined by the steady-state impulse response of the system under weaker assumptions than those of previous works. With a class of asymptotically autonomous systems as a guiding example, it is shown that general invariant manifolds (which do not necessarily pass through the origin) can be also used to characterise moments at a pole. Finally, a dual notion of moment at a pole is introduced and shown to be “natural” for systems in feedforward form.

Keywords: Nonlinear Systems and Control, Feedback Control Systems
Abstract: In this paper, we study the problem of constructing flat inputs for two-output dynamical systems. The notion of flat inputs has been introduced by Waldherr and Zeitz (2008, 2010) and can be seen as a dual perspective for that of flat outputs. In the single-output case, a flat input can be constructed if and only if the original system together with its output is observable. In the multi-output case, the observability is not necessary for the construction of the flat inputs. We start by discussing (from the point of view of minimal differential weight) the case when the dynamical system together with the given output is observable and we present a generalization of the results of Waldherr and Zeitz (2010). Then, we give our main results. We consider the unobservable case for which we study the local and global problems. We completely describe the local case, discuss the issue of the minimal perturbation of the original system, and propose a solution for the global problem. Finally, we explain how our results can be applied to secure communication.

Keywords: Nonlinear Systems and Control, Feedback Control Systems, Hybrid Systems
Abstract: The paper extends the concepts of dominance and p-dissipativity to the non-smooth family of linear complementarity systems. Dominance generalizes incremental stability whereas p-dissipativity generalizes incremental passivity. The generalization aims at an interconnection theory for the design and analysis of switching and oscillatory systems. The approach is illustrated by a detailed study of classical electrical circuits that switch and oscillate.

Keywords: Nonlinear Systems and Control, Mathematical Theory of Networks and Circuits, Operator Theoretic Methods in Systems Theory
Abstract: This paper provides a Fliess operator representation for a class of continuous-time Markov jump nonlinear systems. This representation allows one to describe the parallel sum and product interconnections of such systems. The paper concludes by showing that all parallel interconnections preserves rationality when the component operators have rational generating series.

Keywords: Nonlinear Systems and Control, Stability, Optimization : Theory and Algorithms
Abstract: In this report, we propose an asymptotically stabilizing controller using a control Lyapunov function (clf). The proposed controller generates a sparse input vector, when no input constraint is active, for energy savings. For the cases with no input constraint, the control law can be described explicitly in a variant of Sontag-type controller. When some input constraints are subjected to the system, the control input can be obtained by solving an LP problem. The controller makes the time derivative of the clf negative, if possible. Otherwise, an input minimizing the time derivative of the clf is chosen, where all inputs are saturated. We have also proposed a chattering-suppression mechanism. The effectiveness of the proposed method is confirmed by computer simulations.

Keywords: Adaptive Control, Robust and H-Infinity Control
Abstract: Given a dynamic plant with parametric uncertainty, we present a causal state feedback law, that minimizes the worst case input-output l2-gain. The control law is adaptive in the sense the past data is used to estimate model parameters for prediction of future dynamics. The given formula recovers standard H-infinity optimal state feedback when the parametric uncertainty shrinks to zero.

Keywords: Optimization : Theory and Algorithms, Large Scale Systems, System Identification
Abstract: The optimal mass transport problem has recently gained significant interest in application areas such as signal processing, image processing, and computer vision. Although the problem can be phrased as a linear program, in many cases the resulting optimization problem is intractable due to the vast number of variables. This issue was recently addressed by introducing a perturbation in terms of an entropic barrier term and solving the resulting optimization problem using Sinkhorn iterations. In this extended abstract we extend this to incorporate a class of optimization problems involving an optimal transport cost. In particular we show that the proximal operator of the optimal transport cost can be computed, also for large problems, using Sinkhorn-type iterations. By using a splitting framework, this is then used to solve inverse problems where the optimal mass transport cost is used for incorporating a priori information. We illustrate the method on a problem in limited angle computerized tomography, where a priori information is used to compensate for missing measurements.

Keywords: Optimization : Theory and Algorithms, Large Scale Systems
Abstract: This paper proposes a distributed multi-agent optimization protocol to solve a Pareto optimal problem. The protocol only requires local communications between agents to exchange decision variables and the graph representing the communications has to be only strongly connected but does not need to be balanced. This extends the implementability of the protocol to real-world applications. The protocol is based on exact penalty methods and can handle inequality and equality constraints. The computation is executed without disclosing objective and constraint functions.

Keywords: Optimization : Theory and Algorithms, Large Scale Systems
Abstract: This paper studies the connections between mean-field games and an auxiliary optimization problem, and compares the auxiliary optimization with potential functions. We formulate a large-population game in function space. The cost functions of all agents are weakly coupled though the mean of the population states/controls. We show that under some conditions, the epsilon-Nash equilibrium of the mean-field game is the optimal solution to an auxiliary optimization problem, and this is true even when the optimization problem is non-convex. The result enables us to evaluate the mean-field equilibrium, and also has some interesting implications on the existence, uniqueness and computation of the mean-field equilibrium. While the auxiliary optimization is similar to the potential function in potential games, we show that in general, the mean-field game considered in this paper is not a potential game. We compare the auxiliary optimization problem with potential function minimization, and discuss their differences in terms of solution concept and computation complexity.

Keywords: Optimization : Theory and Algorithms, Signal Processing
Abstract: Low rank matrix completion is the problem of recovering the missing entries of a large data matrix by using the low-rankness assumption. Much attention has been put recently to exploiting correlations between the column/row entities, through side information or data adaptive models, to improve the matrix completion quality. In this paper, we propose a novel graph learning algorithm and apply it to the learning of a graph adjacency matrix from a given, incomplete data matrix, in a way such that the weighted graph edges encode pairwise similarities between the rows/columns of the data matrix. Subsequently we present a graph-regularized low-rank matrix completion method. Experiments on synthetic and real datasets show that this regularized matrix completion approach achieves significant improvement for the matrix completion task.

Keywords: Artificial Intelligence, Optimization : Theory and Algorithms, Stability
Abstract: The aim of this paper is to study the convergence of the primal-dual dynamics pertaining to Support Vector Machines (SVM). The optimization routine, used for determining an SVM for classification, is first formulated as a dynamical system. The dynamical system is constructed such that its equilibrium point is the solution to the SVM optimization problem. It is then shown, using passivity theory, that the dynamical system is global asymptotically stable. In other words, the dynamical system converges onto the optimal solution asymptotically, irrespective of the initial condition. Simulations and computations are provided for corroboration.

Keywords: System Identification, Physical Systems Theory, Process Control
Abstract: The problem of fault detection and isolation in cyber-physical systems is growing in importance following the trend to have an ubiquitous presence of sensors and actuators with network capabilities in power networks and other areas. In this context, attacks to power systems or other vital components providing basic needs might either present a serious threat or at least cost a lot of resources. In this paper, we tackle the problem of having an intruder corrupting a smart grid in two different scenarios: a centralized detector for a portion of the network and a fully distributed solution that only has limited neighbor information. For both cases, differences in strategies using Set-Valued Observers are discussed and theoretical results regarding a bound on the maximum magnitude of the attacker's signal are provided. Performance is assessed through simulation, illustrating, in particular, the detection time for various types of faults in IEEE testbed scenarios.

Keywords: Quantum Control, Stochastic Control and Estimation, Operator Theoretic Methods in Systems Theory
Abstract: This paper considers links between the original risk-sensitive performance criterion for quantum control systems and its recent quadratic-exponential counterpart. We discuss a connection between the minimization of these cost functionals and robustness with respect to uncertainty in system-environment quantum states whose deviation from a nominal state is described in terms of the quantum relative entropy. These relations are similar to those in minimax LQG control for classical systems. The results of the paper can be of use in providing a rational choice of the risk-sensitivity parameter in the context of robust quantum control with entropy theoretic quantification of statistical uncertainty in the system-field state.

Keywords: Stochastic Control and Estimation, Large Scale Systems, Stochastic Modeling and Stochastic Systems Theory
Abstract: This paper investigates the so-called asymptotic solvability problem in linear quadratic (LQ) mean field games. The model has asymptotic solvability if for all sufficiently large population sizes, the corresponding game has a set of feedback Nash strategies subject to a mild regularity requirement. We provide a necessary and sufficient condition and show that in this case the solution converges to a mean field limit. This is accomplished by developing a re-scaling method to derive a low dimensional ordinary differential equation (ODE) system, where a non-symmetric Riccati ODE has a central role.

Keywords: Stochastic Modeling and Stochastic Systems Theory, Information Theory, Discrete Event Systems
Abstract: We define the probability structure of a continuous-time time-homogeneous Markov jump process, on a finite graph, that represents the continuous-time counterpart of the so-called Ruelle-Bowen discrete-time random walk. It constitutes the unique jump process having maximal entropy rate. Moreover, it has the property that, given the number of jumps between any two specified end-points on the graph, the probability of traversing any one of the alternative paths that are consistent with the specified number of jumps and end-points, is the same for all, and thereby depends only on the number of jumps and the end-points and not the particular path being traversed.

Keywords: Stochastic Control and Estimation, Optimal Control, Large Scale Systems
Abstract: This paper studies the existence and uniqueness of a solution to linear quadratic (LQ) mean field social optimization problems with uniform agents. We exploit a Hamiltonian matrix structure of the associated ordinary differential equation (ODE) system and apply a decomposition method to find the solution; this is facilitated by solving a Riccati equation via Schur vectors where the state weight matrix may not be positive semi-definite. We further extend the decomposition method to LQ mean field games.

Keywords: System Identification
Abstract: We relax several assumptions in the model from our previous work that was published in 2016 to model isothermal CO2 adsorption columns based on breakthrough curves and calorimetry measurements. The unknown parameters in the models are determined by minimizing the integral in time of the squared difference between the model prediction and experimental measurement. In a previous effort, only the CO2 adsorption behavior was used to develop the model. In this work, we include calorimetry data to improve the model. Based on the simulation result and theoretical prediction, we conclude that physical adsorption and/or elementary reactions may need to be considered in the model.

Keywords: Coding Theory
Abstract: Constant-dimension subspace codes, which are one of the basic tools in Random Linear (One-Shot) Network Coding, can be easily obtained by lifting rank metric codes. Analogously, convolutional codes for Multi-Shot Network Coding can be based on rank metric convolutional codes. The Authors already established a general framework for the latter kind of codes, defining a suitable (rank) distance, deriving a Singleton-like upper bound, and showing its tightness by means of the concrete construction of Maximum Rank Distance (MRD) convolutional codes. However, the decoding process, that depends on the Viterbi algorithm, may suffer from computational issues. In this contribution, an equivalent construction of a "systematic" rank metric convolutional code will be presented, which permits to simplify both the encoding and the decoding procedures. In particular, the trellis (and, therefore, the decoding) complexity can be reduced under some assumptions on the error patterns.

Keywords: Coding Theory, Information Theory
Abstract: In this paper we address the problem of extending the well-known notion of column distance of one-dimensional (1D) convolutional codes to the context of multidimensional (nD) convolutional codes. In particular, we treat the 2D case and propose a new and more general notion than the one previously introduced in this context. We derive upper bounds on the distances that lead to the novel notion of Maximum Separation Set Distance Profile 2D convolutional codes. This notion naturally extends the notion of Maximum Distance Profile 1D convolutional code. Characterizations in terms of the sliding parity-check matrices are presented.

Keywords: Coding Theory, Information Theory
Abstract: In this preliminary work we investigate the burst erasure-correction capabilities of convolutional codes. In particular, we focus on the class of encoders that admit the shortest possible decoding delay to recover all bursts of erasures of a given length for a given rate. A new simple class of such encoders is presented.

Keywords: Coding Theory, Information Theory
Abstract: In this work we study the problem of list decoding of block codes over finite rings over the erasure channel. We provide explicit formulas for the list decoding size of a linear code over Z_{p^r} and show that this number is determined by the number of independent columns of a series of matrices obtained from the p-adic decomposition of a parity-check matrix of the code. The result is constructive in the sense that it can lead to an algorithm for list decoding of these codes. This work can be considered as a first step toward the study of list decoding over more difficult channels and codes, e.g., convolutional codes.

Keywords: Infinite Dimensional Systems Theory, Robust and H-Infinity Control
Abstract: The Bounded Real Lemma, i.e., the state-space LMI characterization (referred to as Kalman-Yakubovich-Popov or KYP inequality) of when an input/state/output linear system satisfies a dissipation inequality, has recently been studied for infinite-dimensional discrete-time systems in a number of different settings. Here we focus on the Bounded Real Lemma in the context of infinite dimensional, discrete-time, bicausal systems. The transfer functions for such systems need not be stable, and as a result, one expects the solution to the KYP inequality to be only selfadjoint, and not (strictly) positive definite as in the classical case. This indeed turns out to be the case for the bicausal systems we consider. By a variation on Willems' storage-function approach, we prove variations on the standard and strict Bounded Real Lemma, leading to a minimal and maximal solution for the KYP inequality.

Keywords: Applications of Algebraic and Differential Geometry in Systems Theory, Operator Theoretic Methods in Systems Theory, Optimization : Theory and Algorithms
Abstract: The univariate moment problem is an old problem with origins tracing back to work of Stieltjes. The multivariate moment problem has been considered more recently. Even more recently, there has been considerable interest, for both pure theory and applications, in the infinite-variate moment problem, dealing with the moment problem in infinitely many variables. Most of the work has been done so far for the case where the moment functional in question is continuous for a certain topology. In this talk, based on the work of Ghasemi, Kuhlmann, and Marshall 2016 we deal systematically with the general case without any continuity assumptions. The main new concept that we introduce and develop to this end is that of a constructibly Radon measure on the (infinite dimensional) real vector space. The talk will focus on presenting an infinite dimensional generalization of Haviland’s theorem in this setting.

Keywords: Operator Theoretic Methods in Systems Theory, Multidimensional Systems, Applications of Algebraic and Differential Geometry in Systems Theory
Abstract: It is well known that every noncommutative (nc) rational function, of finitely many variables, that is regular at the origin admits a minimal realization and that the stable extended domain of the function is equal to the invertibility set of the pencil of the minimal realization. In addition, a nc power series around the origin will be the power series expansion of a nc rational function if and only if a given Hankel matrix built from the coefficients of the given power series has a finite rank (Fliess-Kronecker).

We present the generalizations of these two results to the case of any nc rational functions, i.e., nc rational functions that are regular at some arbitrary tuple. Those generalizations give a characterization of all nc rational functions, first in terms of their realizations and second in terms of their power series expansions.

Keywords: Multidimensional Systems, Operator Theoretic Methods in Systems Theory
Abstract: In this talk we extend the vessel theory, or equivalently, the theory of overdetermined 2D systems to the Pontryagin space setting. The associated transfer function becomes a mapping with a finite number of negative squares between certain vector bundles defined on a compact Riemann Surface. Furthermore, we present a realization theorem of these mappings. In particular, we develop an indefinite version of the de Branges Rovnyak spaces over real compact Riemann surfaces, i.e. reproducing kernel Pontryagin spaces of analytic sections defined on real compact Riemann surfaces.

Keywords: Linear Systems, Computations in Systems Theory
Abstract: Recently the author has shown an analysis technique of general, not necessarily positive, LTI systems via conversion to externally positive systems. More precisely, the author established a construction method of an externally positive system whose impulse response is given by the square of the original LTI system to be analyzed. Then, it has been proved that the H2 norm computation problem of a general LTI system of order n can be reduced into the L-infinity-induced norm computation problem of an externally positive system of order n^2. On the basis of these preceding results, in this study, we show that the order of the externally positive system can be reduced up to n(n+1)/2 by using the elimination and duplication matrices that are intensively studied by Jan R. Magnus in the 80's. In addition to the computational complexity reduction in dealing with the H2 analysis, we show that such construction of externally positive systems with reduced order is quite effective in semidefinite-programming-based peak value analysis of impulse responses of general LTI systems.

Keywords: Systems on Graphs, Optimal Control, Biological Systems
Abstract: We study the problem of containing epidemic spreading processes in temporal networks. We specifically focus on the problem of finding a resource allocation to suppress epidemic infection, provided that an empirical time-series data of connectivities between nodes is available. Although this problem is of practical relevance, it has not been clear how an empirical time-series data can inform our strategy of resource allocations, due to the computational complexity of the problem. In this direction, we present a computationally efficient framework for finding a resource allocation that satisfies a given budget constraint and achieves a given control performance. The framework is based on convex programming and, moreover, allows the performance measure to be described by a wide class of functionals called posynomials with nonnegative exponents. We illustrate our theoretical results using a data of temporal interaction networks within a primary school.

Keywords: Stochastic Modeling and Stochastic Systems Theory, Linear Systems, Feedback Control Systems
Abstract: This paper deals with Markov Jump Linear Systems (MJLS) with the state constrained in a polyhedral cone. This class of systems can be seen as the generalization of Positive MJLS (where the cone is the positive orthant of the state space). First, we provide results on the analysis of some relevant performance indices, including the expected L1 norm of the impulse response. The problem of state-feedback design preserving cone-invariance and stability while guaranteeing an upper bound of such a performance index is also tackled. Two different solutions are worked out. The first one is based on nonlinear programming but has the advantage of providing a full parametrization of all admissible gains. The second solution is based on linear programming but is more conservative. Some numerical examples are presented to show the effectiveness of these design procedures.

Keywords: Transportation Systems, Linear Systems, Large Scale Systems
Abstract: We study a linear quadratic control problem for a transportation problem on a directed line graph. We show that the solution to the Riccati equation associated with this problem is highly structured. The feedback law is almost triangular, and the synthesis of the feedback law is given by a recursion, making it scalable. The structure of the feedback law also allows for an efficient realization of the controller using a local communication scheme.

Keywords: Linear Systems, Stability
Abstract: This paper investigates the L_{infty}-gain of discrete-time positive periodic systems. By applying the lifting approach, the positive periodic system is transformed into a linear time-invariant positive system. Then based on the L_{infty}-gain characterization of a time-invariant positive systems, an equivalent condition to describe the L_{infty}-gain of positive periodic systems is given. Furthermore, a state-feedback periodic controller to guarantee stability and L_{infty}-gain of the system is obtained by solving linear inequalities. Finally, numerical examples are given to illustrate the theoretical results.

Keywords: Infinite Dimensional Systems Theory, Stability
Abstract: Parabolic-hyperbolic PDE loops present unique features because they combine the finite signal transmission speed of hyperbolic PDEs with the unlimited signal transmission speed of parabolic PDEs. Since there are many possible interconnections that can be considered, it is difficult to give results for a “general case”. The present work focuses on two particular cases, which are analyzed in detail.

The first case is the feedback interconnection of a parabolic PDE with a special first-order hyperbolic PDE: a zero-speed hyperbolic PDE. Thus the action of the hyperbolic PDE resembles the action of an ODE. However, the study of this particular loop is of special interest because it arises in an important application: the movement of chemicals underground. Moreover, the study of this system can be used for the analysis of wave equations with Kelvin-Voigt damping.

The second case is the feedback interconnection of a parabolic PDE with a first-order hyperbolic PDE by means of a combination of boundary and in-domain terms. The interconnection is effected by linear, non-local terms. The study of this case is motivated by the boundary feedback stabilization problem for a system of hyperbolic, first-order PDEs. The study of robustness of the closed-loop system with respect to neglected diffusion phenomena leads to this specific parabolic-hyperbolic PDE loop. The obtained results for this case can also be used for the derivation of delay-independent stability conditions for parabolic PDEs with delayed, nonlocal terms.

For both cases, we provide results for existence/uniqueness of solutions as well as sufficient conditions for ISS or exponential stability in the spatial sup norm. The proof procedures of the obtained results are similar in both cases: a small-gain methodology.

Keywords: Control of Distributed Parameter Systems, Infinite Dimensional Systems Theory, Nonlinear Systems and Control
Abstract: This paper presents two methods for the establishment of ISS estimates in L^q-norm (qgeq 2) for Burgers' equation with different types of boundary disturbances. Precisely, for Burgers' equation with Dirichlet boundary conditions, we use De~Giorgi iteration and Lyapunov method by adequately splitting the original problem into two subsystems to establish the ISS estimates in L^q-norm with some qgeq 2. Whereas, for Burgers' equation with certain nonlinear boundary conditions involving spacial derivatives of the solution, we obtain the ISS estimates in L^2-norm and L^q-norm with any qgeq 2 by some variations of Sobolev embedding inequalities that can be used to deal with the boundary items involved in Lyapunov functionals-based analysis.

Keywords: Control of Distributed Parameter Systems, Stability, Infinite Dimensional Systems Theory
Abstract: In this note, we are concerned with the stabilization of linear port-Hamiltonian systems on an interval (a,b) (for instance, vibrating strings or beams) in the presence of external disturbances. In order to achieve stabilization we couple the system to a nonlinear dynamic boundary controller whose output is allowed to be corrupted by an external disturbance before it is fed back into the system. We first establish the well-posedness of the resulting closed-loop system and then present two input-to-state stability results for the closed-loop system (with input being the external disturbance): for a special class of nonlinear controllers, we obtain uniform input-to-state stability and for a more general class of nonlinear controllers, we obtain weak input-to-stability. Also, in both cases we get convergence of all solutions to zero.

Keywords: Control of Distributed Parameter Systems, Stability, Nonlinear Systems and Control
Abstract: The problem of robust stabilization with bounded feedback control is considered for a scalar reaction-diffusion system with uncertainties in the dynamics. The maximum value of the control input acting on one of the boundary points has to respect a given bound at each time instant. It is shown that, if the initial condition and the disturbance satisfy certain bounds (computed as a function of the bound imposed on the control input), then the proposed control respects the desired saturation level and renders the closed-loop system locally input-to-state stable, that is, the trajectories with certain bound on the initial condition converge to a ball parameterized by certain norm of the disturbance.

Keywords: Nonlinear Systems and Control, Infinite Dimensional Systems Theory, Stability
Abstract: For a broad class of infinite-dimensional systems, we characterize input-to-state practical stability (ISpS) using the uniform limit property and in terms of input-to-state stability. We specialize our results to the systems with Lipschitz continuous flows and evolution equations in Banach spaces. Even for the special case of ordinary differential equations our characterizations of ISpS via the limit property are novel and improve existing criteria for ISpS.

Keywords: Control of Distributed Parameter Systems, Robust and H-Infinity Control, Linear Systems
Abstract: Introduced for finite-dimensional systems by Francis and Wonham in the mid 70's, the internal model principle states that a stabilizing controller achieves asymptotic output tracking and disturbance rejection robustly if and only if it contains a p-copy of the exosystem frequencies, where p is the dimension of the output space of the plant. Later, the internal model principle has been extended, e.g., to boundary control systems on multidimensional spatial domains, and in this setting it follows from the principle that every robust output regulator is necessarily infinite-dimensional. However, it was recently established by the authors that robust emph{approximate} output tracking can be achieved with a finite-dimensional controller, and in the present paper, we formulate an internal model for this purpose. The efficiency of the method is numerically demonstrated using the heat equation on the unit square in mathbb R^2 with boundary control and boundary observation.

Keywords: Control of Distributed Parameter Systems, Stability, Feedback Control Systems
Abstract: In this paper, for a class of linear, distributed port-Hamiltonian systems defined on a one-dimensional spatial domain, an equivalent Brayton-Moser formulation is obtained. The dynamic is expressed as a gradient equation with respect to a new storage function, the "mixed-potential," with the dimensions of power, and the system is passive with respect to a supply rate related to the reactive power. The Brayton-Moser representation is the starting point for the synthesis of boundary control laws whose effect on the system is to shape the mixed-potential function. The general theory is illustrated with the help of an example, namely the boundary stabilisation of longitudinal vibrations of a beam with internal dissipation.

Keywords: Computational Control, Control of Distributed Parameter Systems, Physical Systems Theory
Abstract: We show the application of a recently presented structure-preserving semi-discretization method to the heat equation on an arbitrary dimensional spatial domain. It retains the separation of the geometric (Stokes-)Dirac structure with its global balance equation, from the dynamics and constitutive equations. On the 1D example, we exploit the banded structure of the resulting state space matrices in order to analyze the approximation quality of the eigenvalues for two representative parametrizations. We show that the spatial discretization scheme preserves also a given flat output as a basis for feedforward motion planning.

Keywords: Control of Distributed Parameter Systems, Delay Systems, Stability
Abstract: We consider the Schrödinger equation in a bounded domain of Rn with a delay term in the nonlinear boundary feedback. Under suitable assumptions, we prove global existence of the solutions by the arguments of nonlinear semigroup theory. Moreover, we obtain uniform decay rates for the solutions by following an approach that is based on certain integral inequalities for the energy functional and a comparison theorem that relates the asmptotic behaviour of the energy and of the solutions to a dissipative ordinary differential equation.

Keywords: Control of Distributed Parameter Systems, Nonlinear Systems and Control
Abstract: The output feedback control of distributed parameter systems (DPS) based on adaptive model reduction is explored in this paper. A significant computational hurdle when using model reduction for control is the numerical integration of integrals that appear in the reduced order model reducing their applicability when dealing with nonlinearities. The objective of this paper is to further reduce the computational cost in discrete adaptive proper orthogonal decomposition (DAPOD). It is addressed by using discrete empirical interpolation method (DEIM) in the observer and controller to reduce the computational cost associated with the computation of nonlinear functions. The proposed method is successfully applied in a tubular reactor with recycle.

Keywords: Optimization : Theory and Algorithms, Stochastic Control and Estimation, Applications of Algebraic and Differential Geometry in Systems Theory
Abstract: An optimal mass transport framework on the space of Gaussian mixture models is presented. These models are widely used in statistical inference. We treat such models as discrete measures on the space of Gaussian densities. Our method leads to a natural way to compare and interpolate Gaussian mixture models, with low computational cost. The method represents a first attempt to study optimal transport problems for probability densities with specific structure that can be suitably exploited.

Keywords: Discrete Event Systems, Stochastic Control and Estimation, Optimal Control
Abstract: We propose a method of approximating multivariate Gaussian probabilities using dynamic programming. We show that solving the optimization problem associated with a class of discrete-time finite horizon Markov decision processes with non-Lipschitz cost functions is equivalent to integrating a Gaussian functions over polytopes. An approximation scheme for this class of MDP’s is proposed and explicit error bounds under the supremum norm for the optimal cost to go functions are derived.

Keywords: Mechanical Systems, Optimal Control, System Identification
Abstract: This paper discusses vibration suppression of milling machine tools by the inerter. There are two traditional methods to repress the cutting vibration of milling machines: the passive and the active approaches. The former normally applies mechanical networks consisting of the masses, dampers and springs. However, the mass element is not a genuine two-terminal network element and might restrict the achievable performance of the mechanical networks. Therefore, the inerter is invented to substitute the mass element. This paper investigates the benefits of the inerter in improving the vibration responses of milling machines. First, we conduct identification experiments to obtain the model of a milling machine. Second, we design three passive suspension layouts to illustrate the benefits of the inerter in suppressing the cutting vibration. Last, we conduct experiments to demonstrate the effectiveness of the inerter in improving the manufacturing performance of the milling machine.

Keywords: Optimal Control
Abstract: In this paper a profit optimization between electricity producers is formulated. The problem is described by a linear jump-diffusion system of conditional mean-field type where the conditioning is with respect to common noise and a quadratic cost functional involving the second moment, the square of the conditional expectation of the control actions of the producers. We provide semi-explicit solution of the corresponding mean-field-type game problem with common noise. The equilibrium strategies are in state-and-conditional mean-field feedback form, where the mean-field term is the conditional price given the realization of the global uncertainty.

Keywords: Signal Processing, Optimization : Theory and Algorithms, Robust and H-Infinity Control
Abstract: Phase retrieval finds many applications in signal processing, and recently, there has been a growing interest in directly solving it via nonconvex optimization. Under certain generic statistical models, the loss function satisfies the so- called Regularity Condition (RC) in a local neighborhood of the true signal, which guarantees the linear convergence of gradient descent if initialized properly. However, accelerated first-order methods (e.g. Nesterov’s method and Heavy-ball method), despite the empirical success, currently lack similar performance guarantees as the unaccelerated counterpart. This paper studies the convergence of accelerated first-order meth- ods in phase retrieval using tools from robust control. We derive a set of Linear Matrix Inequalities (LMIs) that can be used to numerically certify linear convergence of accelerated first- order methods under the Regularity Condition. For the Heavy- ball method, analytical conditions of algorithmic parameters for linear convergence are further obtained.