Keywords: Identification for control, Nonlinear systems identification, Data driven control
Abstract: This paper proposes a framework called Iterative Residual Dynamic Mode Decomposition (IRDMD) to address a limitation of extended dynamic mode decomposition (EDMD)---the need to manually select observables. While EDMD provides rich nonlinear representations by embedding state variables into a higher-dimensional space, it suffers from sensitivity to the choice of observables and requires prior knowledge for their design. In contrast, IRDMD automatically constructs observables by iteratively capturing residuals that arise from basic dynamic mode decomposition (DMD) approximations. Furthermore, IRDMD updates the system matrix gradually, making it more computationally efficient than EDMD. We apply IRDMD to both autonomous and control systems and demonstrate its effectiveness in prediction and control tasks through numerical experiments. The results confirm that IRDMD not only enables accurate forecasting but also achieves computationally efficient system identification and control on various nonlinear systems compared to EDMD.

Keywords: Estimation, Identification
Abstract: Within Bayesian state estimation, considerable effort has been devoted to incorporating constraints into state estimation for process optimization, state monitoring, fault detection and control. Nonetheless, in the domain of state-space system identification, the prevalent practice entails constructing models under Gaussian noise assumptions, which can lead to inaccuracies when the noise follows bounded distributions. With the aim of generalizing the Gaussian noise assumption to potentially truncated densities, this paper introduces a method for estimating the noise parameters in a state-space model subject to truncated Gaussian noise. Our proposed data-driven approach is rooted in maximum likelihood principles combined with the Expectation-Maximization algorithm. The efficacy of the proposed approach is supported by a simulation example.

Keywords: Kalman filtering, Fault detection, Nonlinear systems
Abstract: This paper presents a methodology for joint state and fault estimation utilizing a self-tuning extended Kalman filter (EKF). The EKF algorithm builds upon the classical Kalman filter and recursive least squares (RLS) to facilitate simultaneous state and fault estimation. The self-tuning characteristic is incorporated through adaptive mechanisms that address the influence of faults by recursively estimating process and measurement noise covariances using innovation-based covariance matching, as well as by adaptively updating the fault profile matrix via a scaling algorithm. These adaptive strategies are employed to enhance the accuracy of the joint estimation. The effectiveness of the proposed methodology is validated through numerical simulations of a submersible injection pump in a subsea seawater injection system. The results demonstrate significant improvements in estimation performance through adaptive measures, ensuring convergence and robustness. These findings highlight the potential of the proposed approach for real-world fault diagnosis in nonlinear systems.

Keywords: Networked control systems, Control over communications, Network analysis and control
Abstract: Optimal sensor sampling—a key design aspect in sensor and control networks and Internet-of-Things (IoT)— aims for reducing communication load and energy usage. In networked systems where multiple (possibly a large number of) heterogeneous agents use a common communication network to exchange data, network load can be reduced by sampling data only when necessary. Sampling instances are typically optimized such that individual agent’s performance is not substantially degraded, i.e., independent of network conditions. In this letter, we address a network-aware, jointly optimal sampling-control problem for stochastic networked control systems, modeling the network as a dynamical system with memory whose ser- viceability depends on network input, capacity, delays, and dropouts. We define the network state as an indicator of quality and cost of service. The network broadcasts its current and predicted states to agents, who optimize their sampling and control policies accordingly. Agents submit communication requests through their sampling profiles, enabling the network to update its state, and service as many requests as possible in real time. We derive an analytical solution to the optimal control policy, which is independent of network dynamics. In contrast, the optimal sampling policy is tightly coupled with the network state and dynamics, and is the solution of a mixed- integer nonlinear problem. Our theoretical analysis shows that the integer constraint can be relaxed without affecting the optimality.

Keywords: Optimization, Smart grid
Abstract: We consider decision-making problems under decision-dependent uncertainty (DDU), where the distribution of uncertain parameters depends on the decision variables and is only observable through a finite offline dataset. To address this challenge, we formulate a decision-dependent distributionally robust optimization (DD-DRO) problem, and leverage multivariate interpolation techniques along with the Wasserstein metric to construct decision-dependent nominal distributions (thereby decision-dependent ambiguity sets) based on the offline data. We show that the resulting ambiguity sets provide a finite-sample, high-probability guarantee that the true decision-dependent distribution is contained within them. Furthermore, we establish key properties of the DD-DRO framework, including a non-asymptotic out-of-sample performance guarantee, an optimality gap bound, and a tractable reformulation. The practical effectiveness of our approach is demonstrated through numerical experiments on a dynamic pricing problem with nonstationary demand, where the DD-DRO solution produces pricing strategies with guaranteed expected revenue.

Keywords: Adaptive control, Flight control, Lyapunov methods
Abstract: The control of a Dubins Vehicle when subjected to a loss of control effectiveness in the turning rate is considered. A complex state-space representation is used to model the vehicle dynamics. An adaptive control design is proposed, with the underlying stability analysis guaranteeing closed-loop boundedness and tracking of a desired path. It is shown that a path constructed by waypoints and a minimum turn radius can be specified using a reference model which can be followed by the closed loop system. The control design utilizes the complex state-space representation as well as a PID controller for the nominal closed-loop. How the design can be modified to ensure path following even in the presence input constraints is also discussed. Simulation studies are carried out to complement the theoretical derivations.

Keywords: Robust control, Lyapunov methods, Game theory
Abstract: This letter presents a density function based safe control synthesis framework for the pursuit-evasion problem. We extend safety analysis to dynamic unsafe sets by formulating a reach-avoid type pursuit-evasion differential game as a robust safe control problem. Using density functions and semi-algebraic sets, we derive sufficient conditions for weak eventuality and evasion, reformulating the problem into a convex sum-of-squares program solvable via standard semidefinite programming solvers. This approach avoids the computational complexity of solving the Hamilton-Jacobi-Isaacs partial differential equation, offering a scalable and efficient framework. Numerical simulations demonstrate the efficacy of the proposed method.

Keywords: Distributed parameter systems, Flexible structures, Nonlinear systems
Abstract: This paper investigates the preservation of uniform stability for a spatial semi-discrete finite difference scheme applied to a one-dimensional wave equation with nonlinear internal damping. The discretization process employs the order reduction method. Unlike previous studies, this systemfocuses on a nonlinear system, with absolute stability being a special case. Due to the nonlinearity, the system may not always exhibit exponential stability, but it can be polynomially stable in some cases. After semi-discretization, the system transforms into an infinitely large number of lumped parameter nonlinear systems. Achieving uniform polynomial stability, is a challenging endeavor. We demonstrate that when the nonlinear function satisfies certain conditions at the origin and infinity, the system possesses polynomial stability. These properties are preserved during the semi-discretization process. The mathematical proofs are similar to those for the continuous counterpart in many ways.

Keywords: Distributed parameter systems, Backstepping, Differential-algebraic systems
Abstract: This paper considers the backstepping control for a class of general linear infinite-dimensional descriptor systems. By assuming constant matrices in the system description, a decoupling of the descriptor system is possible using the Weierstraß normal form for a matrix pencil with index 1. With this, well-posedness and consistent initial conditions are verified. The resulting decoupled system is a fully actuated hyperbolic-elliptic PDE, where the elliptic PDE can be eliminated by state feedback control. This allows to apply backstepping for the stabilization of a general heterodirectional hyperbolic system with several zero speed states. For the resulting closed-loop system exponential stability is shown. The results of the paper are demonstrated for an unstable infinite-dimensional descriptor system with 6 distributed descriptor variables.

Keywords: Distributed parameter systems, Uncertain systems
Abstract: In a series of papers, the authors developed and refined a cascading-type approximate regulation methodology for symptotic tracking. This method is rooted in the well known geometric theory and involves regularizing the regulator equations with an iterative scheme that generates a sequence of increasingly accurate control laws. One of the main advantages of this method is that no exo-system is required, allowing very general reference and disturbance signals.

Although this earlier approach provided precise tracking and disturbance rejection for complex control systems, similar to the classical regulator method, it was not equipped to handle systems with parameter uncertainties. In this paper, we present a modification of that basic method that ensures accurate tracking and is applicable to a wide range of uncertain systems. The main assumptions include the standard stability condition for both the nominal and perturbed plants and the availability of the tracking error for the uncertain system to the controller. Examples illustrate the theoretical results and demonstrate the method’s effectiveness. Although this paper primarily focuses on distributed parameter systems, the results equally apply to lumped parameter systems.

Keywords: Data driven control, Robust control, Stability of nonlinear systems
Abstract: The growing complexity of dynamical systems and advances in data collection necessitate robust data-driven control strategies without explicit system identification and robust synthesis. Data-driven stability has been explored in linear and nonlinear systems, often by turning the problem into a linear or positive semidefinite program. This letter focuses on contractivity, which refers to the exponential convergence of all system trajectories toward each other under a specified metric. Data-driven closed-loop contractivity has been studied for the case of weighted l2-norms and assuming nonlinearities are Lipschitz bounded in subsets of n-dimensional Euclidean Space. We extend the analysis by considering Riemannian metrics for polynomial dynamics. The key to our derivation is to leverage the convex criteria for closed-loop contraction and duality results to efficiently check infinite dimensional membership constraints. Numerical examples demonstrate the effectiveness of the proposed method for both linear and nonlinear systems.

Keywords: Identification, Subspace methods, Attack Detection
Abstract: This paper is concerned with the partially observed linear system identification, where the goal is to obtain reasonably accurate estimation of the balanced truncation of the true system up to order k from output measurements. We consider the challenging case of system identification under adversarial attacks, where the probability of having an attack at each time is Θ(1/k) while the value of the attack is arbitrary. We first show that the ℓ₁-norm estimator exactly identifies the true Markov parameter matrix for nilpotent systems under any type of attack. We then build on this result to extend it to general systems and show that the estimation error exponentially decays as k grows. The estimated balanced truncation model accordingly shows an exponentially decaying error for the identification of the true system up to a similarity transformation. This work is the first to provide the input-output analysis of the system with partial observations under arbitrary attacks.

Keywords: Subspace methods, Identification, Model/Controller reduction
Abstract: Low-rank matrix regression is a fundamental problem in data science with various applications in systems and control. Nuclear norm regularization has been widely applied to solve this problem due to its convexity. However, it suffers from high computational complexity and the inability to directly specify the rank. This work introduces a novel framework for low-rank matrix regression that addresses both unstructured and Hankel matrices. By decomposing the low-rank matrix into rank-1 bases, the problem is reformulated as an infinite-dimensional sparse learning problem. The least-angle regression (LAR) algorithm is then employed to solve this problem efficiently. For unstructured matrices, a closed-form LAR solution is derived with equivalence to a normalized nuclear norm regularization problem. For Hankel matrices, a real-valued polynomial basis reformulation enables effective LAR implementation. Two numerical examples in network modeling and system realization demonstrate that the proposed approach significantly outperforms the nuclear norm method in terms of estimation accuracy and computational efficiency.

Keywords: Optimization, Optimization algorithms, Machine learning
Abstract: The paper studies decentralized optimization over networks, where agents minimize a composite objective consisting of the sum of smooth convex functions--the agents' losses--and an additional nonsmooth convex extended value function. We propose a decentralized algorithm wherein agents {it adaptively} adjust their stepsize using local backtracking procedures that require no global (network) information or extensive inter-agent communications. Our adaptive decentralized method enjoys robust convergence guarantees, outperforming existing decentralized methods, which are not adaptive. Our design is centered on a three-operator splitting, applied to a reformulation of the optimization problem. This reformulation utilizes a proposed BCV metric, which facilitates decentralized implementation and local stepsize adjustments while guarantying convergence.