Keywords: Stability
Abstract: The phase or argument of a complex number is an elementary yet important concept, essential to almost all scientific disciplines. In SISO signal and system theory the concept of phase used to play an extremely important role. What are the phases of a complex square matrix? The answer does not seem to be unique. In this presentation, we will examine three different definitions: the principal phases (40 year old), the sectorial phases (6 year old), and the segmental phases (new born). We will compare the properties of these phase notions and use them to estimate the eigenvalue phase angles. We will also examine a network and system theory based on the phases, complementing and interconnecting with the existing gain (magnitude, singular value) based theory.

Keywords: Machine Learning and Control, Optimization : Theory and Algorithms, Stochastic Modeling and Stochastic Systems Theory
Abstract: We present a novel kernel-based method for learning multivariate stochastic differential equations (SDEs). The method follows a two-step procedure: we first estimate the drift term function, then the (matrix-valued) diffusion function given the drift. Occupation kernels are integral functionals on a reproducing kernel Hilbert space (RKHS) that aggregate information over a trajectory. Our approach leverages vector-valued occupation kernels for estimating the drift component of the stochastic process. For diffusion estimation, we extend this framework by introducing operator-valued occupation kernels, enabling the estimation of an auxiliary matrix-valued function as a positive semi-definite operator, from which we readily derive the diffusion estimate.

Keywords: Nonlinear Systems and Control, Operator Theoretic Methods in Systems Theory, Stochastic Modeling and Stochastic Systems Theory
Abstract: We present a non-parametric framework for data-driven system identification that learns mappings between input and output paths directly in signature space. Traditional methods often compress output trajectories to scalars, losing geometric information. By embedding truncated path signatures in an operator-valued reproducing-kernel Hilbert space (RKHS), we cast the problem as operator-valued kernel ridge regression. We prove the universality of a weighted Gaussian signature kernel, derive an O(d_Llog d_L/N) non-asymptotic excess-risk bound, and develop a Nyström-based solver that reduces training time from cubic to nearly linear in the sample size. Experiments on a nonlinear stochastic system confirm state-of-the art accuracy with two orders-of-magnitude speed-ups.

Keywords: Operator Theoretic Methods in Systems Theory, System Identification, Nonlinear Systems and Control
Abstract: This manuscript gives a theoretical framework for a new Hilbert space of functions, the so called occupation kernel Hilbert space (OKHS), that operate on collections of signals rather than real or complex numbers. To support this new definition, an explicit class of OKHSs is given through the consideration of a reproducing kernel Hilbert space (RKHS). This space enables the definition of nonlocal operators, such as fractional order Liouville operators, as well as spectral decomposition methods for corresponding fractional order dynamical systems. In this manuscript, a fractional order DMD routine is presented, and the details of the finite rank representations are given. Significantly, despite the added theoretical content through the OKHS formulation, the resultant computations only differ slightly from that of occupation kernel DMD methods for integer order systems posed over RKHSs.

Keywords: Operator Theoretic Methods in Systems Theory, Linear Systems, Multidimensional Systems
Abstract: The theory of dynamical frames arose from practical problems in dynamical sampling where the initial state of a vector needs to be recovered from the space-time samples of future states of the vector. This leads to the investigation of structured frames obtained from the orbits of evolution operators. One of the basic problems in dynamical frame theory is to determine the semigroup representations, which we will call central frame representations, whose frame generators are unique (up to equivalence). In this talk, we will address the general uniqueness problem by presenting a characterization of central frame representations for any semigroup in terms of the co-hyperinvariant subspaces of the left regular representation of the semigroup. This result is not only consistent with the known result of Han and Larson in 2000 for group representation frames, but also proves that the frame vectors for a dynamical frame generated by a k-tuple of bounded commuting operators are equivalent. This is joint work with Deguang Han, Keri Kornelson, David Larson, and Rui Liu.

Keywords: Operator Theoretic Methods in Systems Theory, Information Theory
Abstract: Device-independent quantum random number generation makes use of the intrinsic randomness of quantum processes to generate numbers that are fundamentally unpredictable. The difficulty of controlling quantum systems makes it desirable to harness the full power of the quantum degrees of freedom that one can control. It is known that no more than 2 log d bits of private device-independent randomness can be extracted from a quantum system of local dimension d. This talk presents protocols that achieve this bound for every d. This work is based on joint work with Máté Farkas, Sigurd A. L. Storgaard, Ranyiliu Chen and Laura Mančinska.

Keywords: Information Theory
Abstract: Bell's theorem shows that entangled quantum particles can exhibit correlations that classical particles cannot reproduce without an additional nonlocal resource, such as communication. In this sense, quantum particles are fundamentally more nonlocal than classical ones, and entanglement becomes unavoidable in physics. Here we prove the analogous result within quantum theory itself: indistinguishable fermions transmitted through a quantum network can generate correlations that distinguishable particles or indistinguishable bosons cannot reproduce without additional communication. In the same sense, fermions are fundamentally more nonlocal than bosons or distinguishable particles, motivating fermionic anticommutation and indistinguishability as unavoidable operational resources. Our result further implies that fermions can strictly surpass all qubit-based protocols for certain distributed computing tasks, demonstrating that a complete understanding of information processing requires going beyond qubits to fermionic information carriers - febits.

Keywords: Operator Theoretic Methods in Systems Theory, Quantum Control, Information Theory
Abstract: A constraint satisfaction problem (CSP) is a decision problem where one needs to decide if a given systems of equations admits a solution. CSPs capture some fundamental computational problems, including linear equations, graph colourings, and variants and generalisations of satisfiability. A CSP can be presented via nonlocal games, so an entangled version of the CSP arises via the quantum strategies for this game. Due to the equality of complexity classes MIP*=RE, entangled CSPs can be undecidable, but this is not true of all of them. The current proof techniques to show undecidability of entangled CSPs are quantisations of the gadget reductions used to show NP-completeness of classical CSPs. These techniques rely on commutativity gadgets, which allow the CSP to express any classically achievable relation in the entangled setting. In this work, we show that there exist CSPs that do not admit a commutativity gadget and study the conditions under which CSPs admit commutativity gadgets. This implies that their complexity cannot be ascertained by directly lifting classical reductions, but will need natively quantum and perhaps more subtle reductions. Another possibility is that there may be classically hard CSPs that become easy in the quantum setting. We make use of quantum symmetries of the CSP to ascertain whether it admits a commutativity gadget, and hence whether the classical reductions lift to the quantum setting.

Keywords: Mathematical Theory of Networks and Circuits, Information Theory, Quantum Control
Abstract: As early as 1935, Schrödinger recognized entanglement as "not *one*, but rather *the* characteristic trait of quantum mechanics, the one that enforces its entire departure from classical lines of thought". Indeed, most remarkable phenomena in quantum information science, such as quantum computing and quantum teleportation, spring from clever uses of entanglement. Among them, pseudotelepathy enables two or more players to win systematically at some cooperative games with no need for communication between them, a restriction that would make the task impossible in a classical world. We investigate the power of multipartite entanglement for pseudotelepathy. Some known games that can be won with tripartite entanglement cannot be won with bipartite entanglement, but they can be won with bipartite non-signalling resources such as the so-called Popescu–Rohrlich nonlocal box. We exhibit a five-player game that can be won with tripartite entanglement, but not with arbitrary bipartite non-signalling resources even in the presence of arbitrary five-partite classical resources. This illustrates both the power of bipartite non-signalling resources (over bipartite entanglement) and the even superior power of tripartite entanglement.

Keywords: Control of Distributed Parameter Systems, Stability
Abstract: This note is concerned with the well-posedness and stability of a one-dimensional linear Schrödinger equation in a bounded interval. We assume the presence of an infinite memory term and a localized damping control. Using two different approaches, we show that the problem is well-posed. Furthermore, the asymptotic behavior of the solutions is deduced.

Keywords: Control of Distributed Parameter Systems, Delay Systems, Robust and H-Infinity Control
Abstract: The presentation addresses the boundary control of a class of hyperbolic PDEs, based on an equivalent representation in terms of an integral-difference equation. The situation is considered where direct compensation of reflection terms induces a fragile closed-loop system, in the sense of lack of strong stability. This problem is theoretically resolved by adding a low-pass filter to the control law, but the choice of its cut-off frequency is crucial in balancing robustness at high frequencies and performance at low frequencies. First, a result is presented on the exponential stability for small values of T, the inverse of the filter's cutoff frequency, thus demonstrating the efficacy of the filter. Next, model mismatch on the PDE parameters is considered and a sufficient stability condition is given in terms of allowable mismatch and cut-off frequency, satisfied in a region in the combined parameter space with a conic shape around T=0. Finally, this qualitative behavior is confirmed by exact stability charts for a special case where all model mismatch is contained into one scalar parameter. The fractal nature of the set of stability crossing curves is highlighted.

Keywords: Control of Distributed Parameter Systems, Nonlinear Systems and Control, Infinite Dimensional Systems Theory
Abstract: This paper investigates the approximate multiplicative (bilinear) controllability of parabolic partial differential equations, focusing on a special form of the one-dimensional Fokker-Planck equation. We first derive some properties of weak derivatives, which are used to extend some results of Sturm-Liouville theory to Sobolev spaces, and then establish a relationship between the control through the advection term and the control through the reaction term by means of a suitable transformation. The proposed method is constructive, and it leads to an implementable algorithm for finding a bilinear control through the advection term.

Keywords: Infinite Dimensional Systems Theory, Linear Systems, Stability
Abstract: In this paper, we establish the exponential stability of interior degenerate parabolic equations under a class of relatively bounded perturbations. Our analysis relies on an abstract robustness result for exponentially stable semigroups, appropriate Hardy-Poincaré inequalities, LaSalle’s invariance principle and a unique continuation property for elliptic operators. The study is divided into two main parts, depending on whether the principal diffusion operator is formulated in divergence or in non-divergence form.

Keywords: Control of Distributed Parameter Systems, Stability, Delay Systems
Abstract: In this paper, we study a coupled system of two plate equations. One equation includes both damping and delay terms, while the other is conservative. We show that if the gain of the delayed damping term is smaller than that of the undelayed one, then the strong solution of the closed-loop system is both strongly and polynomially stable. Explicit decay rates are derived, and their optimality is discussed. In other cases, instability results are established by constructing specific sequences of delays and initial data.

Keywords: Optimal Control, Optimization : Theory and Algorithms, Stochastic Control and Estimation
Abstract: We consider a Schrodinger bridge problem where the Markov process is subject to parameter perturbations, forming an ensemble of systems. Our objective is to steer this ensemble from the initial distribution to the final distribution using controls robust to the parameter perturbations. Utilizing the path integral formalism, we demonstrate that the optimal control is a non-Markovian strategy, specifically a stochastic feedforward control, which depends on past and present noise. This unexpected deviation from established strategies for Schrodinger bridge problems highlights the intricate interrelationships present in the system’s dynamics. Furthermore, built on a recent technique known as flow matching in generative AI, we develop a scalable algorithm to compute the optimal control.

Keywords: Optimization : Theory and Algorithms, Stochastic Modeling and Stochastic Systems Theory
Abstract: For a given ground cost, the Monge optimal transport map realizes the pushforward of a given probability measure onto another. The fourth-order Ma-Trudinger-Wang (MTW) tensor associated with this ground cost provides a notion of curvature in optimal transport. In particular, the non-negativity of the MTW tensor becomes important for establishing continuity of the Monge optimal transport map. However, analytically verifying the non-negativity of MTW tensor is extremely challenging, and as a result, such results have so far been demonstrated for relatively simple ground costs. To expand the class of ground cost functions for which MTW non-negativity can be verified, we propose a computational approach which provides certificates of non-negativity for the MTW tensor using Sum-of-Squares (SOS) programming. Within the proposed computational framework, we call this verification as the solution of forward problem. The proposed method is also shown to be useful for solving the inverse problem--where our SOS technique can compute an inner approximation of the region where MTW non-negativity holds, i.e., provides local certificates.

Keywords: Optimization : Theory and Algorithms, Machine Learning and Control
Abstract: We analyze the discrete Monge–Kantorovich problem as well as its generalization to the setting of the diffeomorphism group of the annulus. We link it with the minimization problem of linear functionals over adjoint orbits as well as to convexity of the momentum map and the Schur-Horn theorem in particular. We also discuss the relationship of the optimization problem to dynamics, in particular double bracket on adjoint orbits and the discrete and dispersionless Toda lattice flows.

Keywords: Stochastic Control and Estimation
Abstract: Adapted optimal transport is a recently developed version of optimal transport tailored to the needs of stochastic analysis and mathematical finance. We study the Gaussian case under which explicit computations are possible. This leads to a novel extension of the Bures--Wasserstein distance to the adapted setting.

Keywords: Stochastic Control and Estimation, Optimal Control, Optimization : Theory and Algorithms
Abstract: The dynamic formulation of Monge–Kantorovich transport endows the space of probability measures with a rich geometric structure and has catalyzed advances across control, fluid mechanics, and computation. Motivated by an apparent analogy between the concept of shear in fluid dynamics and that of Brockett’s ‘attention’ functional of a control law, we study a new class of variational problems for optimal transport. The present work develops this type of transport based on the basic Gauss-Markov paradigm of steering Gaussian distributions between specified marginal distributions. Specifically, we consider the flow generated by a linear drift U(t,x) = Atx for Gauss–Markov models and seek to design the control gain At so as to steer the law between the prescribed Gaussian marginals while minimizing a functional that combines spatial and temporal quadratic costs. The terms in the functional consist of the gradient and the time-derivative of the control action. Individually, these two terms penalize a notion of ‘attention’ that a controller needs to dedicate in differentiating with respect to space and time, respectively. In contrast to the classical Monge-Kantorovich transport, the resulting optimization is nonconvex. Yet, the Gaussian structure enables a tractable characterization of optimal solutions and their existence under suitable conditions. The new formalism provides an “attention-penalized” counterpart to Wasserstein-2 transport and suggests connections to shear- penalized geodesic models of fluid flow.

Keywords: Stochastic control, Monge-Kantorovich Transport, Attention-minimizing control

AMS Classification: Primary 49Q22; Secondary 93E20, 60H10.

Keywords: Machine Learning and Control
Abstract: I discuss a cohesive dynamical systems view of reinforcement learning as a methodology for feedback control, organized around three central questions: when learning dynamics converge, when the resulting closed loop remains stable, and how much data is required to achieve reliable performance. I present a high-level synthesis of how these strands fit together into a principled foundation for reinforcement learning in control, and highlight a few open challenges and directions.

Keywords: Networked Control Systems
Abstract: Dynamic games provide a powerful framework for modeling interactions between multiple decision-makers. However, as infinite-dimensional problems, they are notoriously difficult to solve, and the coupling between players can generate emergent behaviours that are difficult to predict. In this talk, we will revisit some basics of dynamic games and (single-player) optimal control. Then, starting with the class of Linear Quadratic dynamic games, we will present iterative algorithms for obtaining feedback Nash equilibrium solutions that are amenable to both model-based and data-driven implementations. Turning our attention to general, nonlinear dynamic games we will then demonstrate how feedback Nash equilibria can be characterised in terms of invariant manifolds of a certain "lifted" dynamical system. This geometric perspective — analogous to the state/costate dynamics associated with Pontryagin's Minimum Principle (e.g. in the context of optimal control and open-loop Nash equilibria of dynamic games) — offers two key advantages. First, it allows us to recast the problem of obtaining feedback Nash equilibria as a static optimisation problem, which lays the basis for novel computational strategies, e.g. based on gradient-descent algorithms. Second, it provides a framework to analyse interactions between players in terms of energy exchange.

Keywords: Neural Networks, Machine Learning and Control, Multidimensional Systems
Abstract: Deep neural networks are powerful tools in science and engineering, but training highly accurate models becomes challenging as problem complexity increases. To address these challenges, we present a progressive framework for training and tuning high-precision neural networks (HiPreNets). Our approach, inspired by the philosophy of learning from previous errors, improves an existing network by sequentially learning its prediction residuals using additional networks, leading to improved overall accuracy. We additionally discuss how to take advantage of the structure of the residuals to guide the choice of loss function. We validate the framework on a benchmark regression problem and a high-dimensional dynamical system based in power systems, where we observe significant accuracy gains.

Keywords: Machine Learning and Control, Neural Networks, Optimal Control
Abstract: Inverse optimal control provides a powerful framework for data-based modeling of optimally controlled processes, as it identifies cost functions for optimal control problems explaining the observed data by their optimal solutions. This work addresses nonlinear infinite-horizon optimal control problems and proposes a neural network-based algorithm for the simultaneous reconstruction of the underlying cost functions and stabilizing feedback laws from pure state data. The approach integrates data fidelity with stability constraints to ensure physically meaningful solutions. We explicitly consider Lyapunov-based constraints and approximate the value function by an adaptive grid refinement strategy integrated into the neural network training. Numerical experiments demonstrate the effectiveness of the method for different systems and under varying noise levels.

Keywords: Model Predictive Control, Optimization : Theory and Algorithms, Machine Learning and Control
Abstract: Dual decomposition is a well-established algorithm to solve strictly convex optimization problems in decentralized fashion. However, as dual decomposition is a first-order method, it often takes a significant number of iterations to converge to acceptable accuracy. We propose a novel dual warm-starting strategy based on learning a predictor of the optimal dual variable of the consensus constraints. We use Gaussian process regression to learn the predictor from pre-computed data. Furthermore, we exploit the posterior variance error bounds of Gaussian Processes and draw upon numerical examples to illustrate the advantages of our approach.

Keywords: Optimal Control, Machine Learning and Control, Neural Networks
Abstract: Optimal control problems become parametric when their constraints or dynamics depend on external parameters. Multiple objectives require a multiobjective formulation, and scalarizing it introduces further parametric dependencies. We propose a grid-free method to model the mapping from parameters to optimal solutions. Using few training samples, we obtain a neural network by combining (i) a KKT-residual loss penalizing first-order optimality violations under standard constraint qualifications, (ii) problem-specific output activations that enforce simple constraints by construction, and (iii) single-shooting-like state simulations within the network. On a trajectory-generation case study with a moving obstacle and competing objectives, the method generalizes to unseen parameters, attaining lower primal error and fewer constraint violations than interpolation and penalty-based training, and recovers the dual variables.

Keywords: Machine Learning and Control, Neural Networks, System Identification
Abstract: This work proposes a probabilistic framework for learning finite-dimensional bilinear Koopman generator models without prescribing an observable dictionary or imposing linear measurement structure. The unknown nonlinear system is modeled as a latent-variable bilinear state–space system whose lifted dynamics approximate a Koopman generator, while measurements are reconstructed through a nonlinear neural-network decoder. The resulting formulation admits a hidden Markov model representation and is identified using a Neural Expectation–Maximization algorithm that combines extended Kalman filtering and smoothing for latent-state inference with closed-form updates of Koopman generator matrices and gradient-based learning of the decoder.

Keywords: Information Theory
Abstract: The set of unital quantum channels on M_n is the natural quantum information theoretic analogue of the convex set of bistochastic matrices in M_n.  For bistochastic matrices, we have the well-known Birkhoff-von Neumann theorem (B-vN theorem) which says that any bistochastic matrix is a convex combination of permutation matrices.  For unital quantum channels, the situation is much more complicated.  For instance, several attempts at a quantum version of Birkhoff's theorem are known to fail (e.g., based on mixed unitary channels or more generally factorizable maps).  In this talk, we will look at unital quantum channels from the perspective of noncommutative (a.k.a. matrix) convexity - viewing unital channels as the first level of an enriched matricial convex structure.  This naturally leads to a new nc convex set of unital channels we call ``mixed quantum unitary channels'', whose nc extreme points are given by quantum automorphisms of M_n.  For some time, we conjectured that mixed quantum unitary channels would provide the correct framework for a quantum B-vN theorem, but our hopes have been dashed once again! I will present some examples of unital channels which fail to be mixed quantum unitary.  Time permitting, I will also explain some consequences this result has on the structure of the operator space spanned by the generators of the free unitary quantum groups. 

This is joint work with Jason Crann and Alec Gow.

Keywords: Information Theory, Quantum Control, Operator Theoretic Methods in Systems Theory
Abstract: We show that the quantum smooth label cover problem is undecidable and RE-hard. This sharply contrasts the quantum unique label cover problem, which can be decided efficiently by a result of Kempe, Regev, and Toner (FOCS'08). On the other hand, our result aligns with the RE-hardness of the quantum label cover problem, which follows from the celebrated MIP* = RE result of Ji, Natarajan, Vidick, Wright, and Yuen (ACM'21). Additionally, we show that the quantum oracularized smooth label cover problem is RE-hard. Our second result fits with the alternative quantum unique games conjecture recently proposed by Mousavi and Spirig (ITCS'25) on the RE-hardness of the quantum oracularized unique label cover problem. Our proof techniques include a quantum version of Feige's reduction from 3SAT to 3SAT5 (STOC'96) for BCSMIP*-protocols, which may be of independent interest.

Keywords: Quantum Control, Operator Theoretic Methods in Systems Theory
Abstract: Parallelization is a fundamental aspect of computation. In quantum computing it is very badly understood. A dramatic illustration of this fact is a very pessimistic conjecture in the 1998 by Cristopher Moore and Martin Nilsson, c.f. Moore and Nilsson (2001), the paper which initiated the study of concrete quantum circuit complexity. They define a class of circuits which look like a staircase with each step consisting of a controlled one qubit unitary. This circuit has n- layers of computation that must be done in sequence: you cannot start a computation at layer r without finishing the first r − 1 layers of computation. Here C(U) denotes the unitary produced by the circuit.

This talk describes how one constructs C(U) as a circuit which asymptotically has depth O(log(n)). The focus is on the following theorem and extensions of it.

Theorem 1. (Adam Bene Watts, Charles Chen, Bill Helton and Joe Slote, to appear STOC 2026). Any unitary matrix C(U) coming from a Moore-Nilsson staircase on n qubits can be produced exactly by an O(log n)-depth, ancilla-free (no extra qubits) circuit.

This presentation (with Adam Bene Watts and Joe Slote) of our strong refutation of the Moore–Nilsson Conjecture will attempt to be accessible to those who are not knowledgable about quantum circuits.

Keywords: Quantum Control, Multidimensional Systems, Signal Processing
Abstract: A central task in quantum information science is state certification: testing that an unknown state is close to a fixed target state. Recent work gives surprisingly simple protocols---comprising only single-qubit measurements---for state certification. However, these protocols are not robust: they can only positively certify states within O(1/n) trace distance to the target, whereas in many experimental settings the appropriate error tolerance is constant. We present protocols robustly certifying almost all pure target states while utilizing small measurements. Our tests are based on a new uncertainty principle for conditional fidelities which may be of independent interest.

Keywords: Optimal Control, Stability, Control of Distributed Parameter Systems
Abstract: This paper develops a Lyapunov-based pointwise convex optimization framework for boundary control of a 1-D wave equation and its cascade with an integral-action ODE under magnitude-bounded actuation. For the wave equation, a parameterized Lyapunov functional yields an explicit dissipation inequality, an explicit stabilizing input interval, and a unique minimum-norm input computed online by solving a pointwise convex quadratic program. A barrier functional enforces forward invariance of an energy-based safe set, and actuator bounds are incorporated by interval intersection. For the cascade, a forwarding coordinate motivates a projection-based boundary feedback that preserves invariance and stabilizes the cascade under an online feasibility condition.

Keywords: Control of Distributed Parameter Systems, Stability, Linear Systems
Abstract: An optimal state observer design problem for a diffusion system with point observation is studied. As the considered system is positive, the analysis takes into account this additional condition. The solution of the optimization problem is derived by means of a discretization approach, which consists in considering the analogous problem adapted for a spatially discretized version of the pure diffusion system.

Keywords: Control of Distributed Parameter Systems, Optimal Control, Transportation Systems
Abstract: In this paper, we study the feasibility of a class of optimization-based boundary control of one-dimensional macroscopic traffic flow models, where stability and invariance are achieved by a single boundary control. We define the sets of controllers to stabilize the system to a desired state via Lyapunov functionals, and to ensure forward invariance of a desired subset via boundary control barrier functionals. The control input is then selected from the intersection of those sets via a convex optimization problem. We determine sufficient conditions to ensure the existence of an optimal boundary control problem achieving both stability and invariance for a generic traffic flux function. Simulation results showcase the behavior of the proposed optimization-based controller applied to conservation laws with several traffic flow functions.

Keywords: Control of Distributed Parameter Systems, Optimal Control, Robotics
Abstract: We present a Model Predictive Control-based optimal control strategy for a swarm distribution to track a time-varying target distribution in the context of the Fokker-Planck–optimal control framework. The control, dependent on both time and space, appears as a drift term in the stochastic differential equation that describes the evolution of the agents. The main contribution is to design a Finite Element Method discretization formulation using the first-discretize-then-optimize approach for our 2D problem. We provide results for both static and time-varying target distributions, along with the convergence error.

Keywords: Control of Distributed Parameter Systems, Optimal Control, Nonlinear Systems and Control
Abstract: We investigate an optimal mixing problem for a passive scalar advected by an incompressible flow in two dimensions. The velocity field is represented as a finite superposition of smooth cellular flows, whose time-dependent intensities serve as control inputs. To promote temporal sparsity of the control actions, we incorporate an L^1-regularization term into the objective functional. This leads to a transport equation driven by sparse actuation and results in a bilinear optimal control problem. We derive the first-order necessary optimality conditions using tools from nonsmooth analysis.

Keywords: Infinite Dimensional Systems Theory, Large Scale Systems, Linear Systems
Abstract: We propose a direct data-driven method for controller synthesis of infinite networks composed of unknown linear time-invariant subsystems. Using a single set of noise-corrupted input-state trajectories collected from each subsystem, and provided that certain linear matrix inequalities hold, each subsystem is rendered exponentially input-to-state stable (eISS) by locally constructing an eISS control Lyapunov function together with an exponentially input-to-state stabilizing feedback controller. We then compose these local components under a compositional small-gain condition in infinite-dimensional spaces to obtain a global control Lyapunov function and an associated stabilizing controller, ensuring uniform global exponential stability of the infinite network. The approach is validated on a physical case study with unknown dynamics.

Keywords: Networked Control Systems, Stochastic Control and Estimation, Large Scale Systems
Abstract: We study strategic interaction in linear-quadratic network games where agents act on subjective, misspecified models of their environment. Agents observe noisy aggregate signals generated by local network externalities and interpret them through simplified conjectures, such as constant or mean-field representations. We characterize the long-run behavior using the Berk-Nash equilibrium (BNE) concept, establishing conditions under which BNE diverges from the Nash equilibrium of the perfectly specified game. We quantify this divergence using a Value of Misspecification (VoM) metric. Building on this framework, we introduce cognitive arbitrage—a design paradigm where a system designer strategically shapes agents' conjectures via minimal observation distortions to steer equilibrium outcomes. We formulate the cognitive arbitrage problem as a Stackelberg optimization with closed-form solutions and prove the convergence of a two-time-scale learning algorithm to the optimal BNE. Our results provide a principled framework for influencing behavior in networked systems with bounded rationality, offering a new perspective on mechanism design that operates on agents' representations rather than their incentives.

Keywords: Networked Control Systems, Feedback Control Systems, Linear Systems
Abstract: We propose a distributed two-degrees-of-freedom (2DOF) architecture for driving autonomous, possibly heterogeneous, agents to agreement. The scheme mirrors classical servo structures, separating local feedback from network filtering. This separation enables independent network-filter design for prescribed noise attenuation and allows controller heterogeneity to reject local disturbances, including disturbances exciting unstable agreement poles -- which is known to be impossible via standard diffusive couplings. The potential of the framework is illustrated via two numerical examples.

Keywords: Networked Control Systems, Nonlinear Systems and Control, Dissipativity
Abstract: This work provides compositional conditions for k-dominance for a class of interconnected nonlinear systems. We show that if a k-dissipation matrix encoding both the interconnection structure and the k_i-passivity indices of the subsystems is diagonally stable, then the interconnected system is k-dominant with k being the sum of all k_i. This generalizes the dominance interconnection theory with a diagonal stability condition. We also introduce an output dominance result: under an incremental observability condition, a dominance inequality with a strict output term is sufficient to characterize the asymptotic flow on compact w-limit sets by a k-dimensional Lipschitz system. The results are illustrated on the Goodwin oscillator, where the proposed conditions establish two-dimensional asymptotic behavior and, together with instability of the unique equilibrium and boundedness in the positive orthant, almost global convergence to a limit cycle.

Keywords: Networked Control Systems, Feedback Control Systems, Linear Systems
Abstract: This paper analyzes the impact of frequency modulation (FM) on control performance when FM is used to transmit signals in feedback loops. We develop an analytical characterization of quadrature FM detection and derive explicit upper bounds on demodulation errors for single-channel and multiplexed transmissions, including additive disturbances. The resulting performance deviation is quantified via the difference between modulated and nominal closed-loop outputs, providing design guidance for modulation and demodulation parameters.