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In this paper, we introduce a set representation called polynomial logical zonotopes for performing exact and computationally efficient reachability analysis on logical systems. We prove that through this polynomial-like construction, we are able to perform all of the fundamental logical operations (XOR, NOT, XNOR, AND, NAND, OR, NOR) between sets of points exactly in a reduced space, i.e., generator space with reduced complexity. Polynomial logical zonotopes are a generalization of logical zonotopes, which are able to represent up to $2^{\gamma }$ binary vectors using only $\gamma$ generators. Due to their construction, logical zonotopes are only able to support exact computations of some logical operations (XOR, NOT, XNOR), while other operations (AND, NAND, OR, NOR) result in over-approximations in the generator space. In order to perform all fundamental logical operations exactly, we formulate a generalization of logical zonotopes that is constructed by dependent generators and exponent matrices. While we are able to perform all of the logical operations exactly, this comes with a slight increase in computational complexity compared to logical zonotopes. To illustrate and showcase the computational benefits of polynomial logical zonotopes, we present the results of performing reachability analysis on two use cases: (1) safety verification of an intersection crossing protocol and (2) reachability analysis on a high-dimensional Boolean function. Moreover, to highlight the extensibility of logical zonotopes, we include an additional use case where we perform a computationally tractable exhaustive search for the key of a linear feedback shift register.

The paper focuses on the set-estimation for uncertain Max-Plus Linear systems, with bounded random parameters. This estimation process involves determining the conditional reach set, which is a compact set of all possible states that can be reached from a previous set through the transition model (dynamics) and can lead to the observed measurements through the observation model. In the context of Bayesian estimation theory, this set represents the support of the posterior probability density function of the system’s state. We compare two approaches, a disjunctive approach, presented in literature, and a concise approach, presented as a contribution of this paper, to exactly compute this set. Even if both approaches are with an exponential theoretical complexity, it is shown that the concise approach is more efficient.

This paper focuses on the boundary stabilization control of a rotating disk–beam–mass system (DBMS), comprised of a one-dimensional flexible beam perpendicularly affixed to a rotating rigid disk at its lower boundary and a payload, conceptualized as a tip mass at its opposite end. We posit that the boundary control, which includes an external torque acting on the disk and an external force acting on the tip mass, is subject to an undefined time-varying disturbance. Concurrently, the flexible beam experiences an undefined spatiotemporal-varying distributed disturbance. Firstly, we employ Hamilton’s principle to elaborate on the mathematical model that describes the motion of DBMS. Subsequently, an adaptive boundary control is designed to stabilize the beam’s transverse displacement and regulate the disk’s angular velocity to track a predetermined value asymptotically. Applying the theory of Lyapunov, we demonstrate that uniform and ultimate boundedness under distributed disturbance can be achieved. Finally, we conduct several numerical simulations to showcase the applicability and efficacy of our proposed adaptive boundary controller.

This paper presents a unified least-squares approach to simultaneous input and state estimation (SISE) of discrete-time linear systems. Although input estimators for systems with and without direct feedthrough are generally designed in two different ways, i.e., one with and another without a delay, the proposed approach unifies the two cases using a receding horizon estimation strategy. Moreover, regularization terms representing input information are incorporated and discarded to accommodate the model-based and model-free scenarios, respectively. The present work first investigates the general case where prior input information is available for systems with direct feedthrough and addresses important issues including the existence, optimality and stability of the derived estimators. Then, the problem of whether and under what conditions the existing studies for different systems can be related together is investigated. By setting different design parameters, the proposed estimation framework includes important literature results as its special cases, making it possible to generalize the SISE problems in various contexts. Besides, unlike the previous studies that only considered recursive SISE formulations, the present study develops a batch SISE (BSISE) formulation that addresses the optimal filtering and smoothing problems cohesively. The present work provides a unified approach to input and state estimation where the availability of the input information ranges from exactly known to completely unknown and the systems may have either zero, non-full-rank or full-rank direct feedthrough. The optimization-based formulation and its Bayesian interpretation open a variety of possible extensions and inspire new developments.

The present paper is devoted to sampled-data control design of a PDE–PDE cascade system. These PDEs are governed by heat equations with different reaction coefficients. In order to stabilize the cascaded heat–heat system, we start with the design of continuous-time feedback control law. Then sampled-data control is further proposed for practical reasons. Sufficient conditions are derived for guaranteeing the exponential stability and well-posedness of the corresponding closed-loop system via Lyapunov method and modal decomposition method. Numerical examples illustrate the efficiency of the proposed method.

This article addresses the problem of optimal deception attacks against remote state estimation, where the measurement data is transmitted through an unreliable wireless channel. A malicious adversary can intercept and tamper with raw data to maximize estimation quality degradation and deceive ${\chi }^2$ detectors. In contrast to prior studies that concentrate on greedy attack performance, we consider a more general scenario where attackers aim to maximize the sum of estimation errors within a fixed interval. It is demonstrated that the optimal attack policy, based on information-theoretic principles, is a linear combination of minimum mean-square error estimates of historical prediction errors. The combination coefficients are then obtained by solving a convex optimization problem. Furthermore, the proposed attack approach is extended to deceive multiple-step ${\chi }^2$ detectors of varying widths with strict/relaxed stealthiness by slightly adjusting some linear equality constraints. The effectiveness of the proposed approach is validated through numerical examples and comparative studies with existing methods.

In this paper, finite-time stabilization is investigated for a class of non-local Lipschitzian large-scale stochastic nonlinear systems with two types of uncertainties, including parametric uncertainties and uncertain interactions. First, we present a new stochastic finite-time stability theorem on stochastic adaptive finite-time control, by which we obtain an existing finite-time stability result for the interconnected stochastic nonlinear systems. Then, for a class of large-scale stochastic nonlinear systems with uncertainties, an adaptive finite-time controller is constructively designed. It is proved by the developed finite-time stability theorem that there exists a global weak solution to the closed-loop system, the trivial weak solution of the closed-loop system is globally stable in probability and the states of the system almost surely converge to the origin in finite time. At last, a simulation example is given to show the effectiveness of the proposed design procedure.

Disturbances in iterative learning control (ILC) may be amplified if these vary from one iteration to the next, and reducing this amplification typically reduces the convergence speed. The aim of this paper is to resolve this trade-off and achieve fast convergence, robustness and small converged errors in ILC. A nonlinear learning approach is presented that uses the difference in amplitude characteristics of repeating and varying disturbances to adapt the learning gain. Monotonic convergence of the nonlinear ILC algorithm is established, resulting in a systematic design procedure. Application of the proposed algorithm demonstrates both fast convergence and small errors.

How to develop control design methods directly based on the input and output data, instead of utilizing the system model, becomes a practically important topic in the control community. This paper explores the data informativity for the data-based control design methods, with a special focus on accomplishing the tracking objective for iterative learning control (ILC) systems. With the data collected under a certain test framework for ILC systems, a necessary and sufficient condition on the data informativity is provided for trackability of the desired reference, which is a premise for the realization of the perfect tracking objective. Based on the informative data for trackability, three classes of data-based ILC updating laws are designed to reach the perfect tracking objective for a group of ILC systems compatible with the informative data. Moreover, the data informativity for $\delta$-trackability of the desired reference is discussed with the focus on the more general $\delta$-tracking objective, under which a data-based ILC updating law is presented by only resorting to the informative data for $\delta$-trackability. In addition, for ILC systems with noises, the collected noisy data are leveraged to further exploit an ILC updating law to achieve the robust tracking objective. All the developed data-based ILC updating laws are applicable for any linear ILC system despite whether it is irregular or not, where the specific system model is not required.

In this paper, the optimal control problem of a class of unknown Markov jump systems (MJSs) is investigated via the parallel policy iteration-based reinforcement learning (PPI-RL) algorithms. First, by solving the linear parallel Lyapunov equation, a model-based PPI-RL algorithm is studied to learn the solution of nonlinear coupled algebraic Riccati equation (CARE) of MJSs with known dynamics, thereby updating the optimal control gain. Then, a novel partially model-free PPI-RL algorithm is proposed for the scenario that the dynamics of the MJS is partially unknown, in which the optimal solution of CARE is learned via the mixed input–output data of all modes. Furthermore, for the MJS with completely unknown dynamics, a completely model-free PPI-RL algorithm is developed to get the optimal control gain by removing the dependence of model information in the process of solving the optimal solution of CARE. It is proved that the proposed PPI-RL algorithms converge to the unique optimal solution of CARE for MJSs with known, partially unknown, and completely unknown dynamics, respectively. Finally, simulation results are illustrated to show the feasibility and effectiveness of the PPI-RL algorithms.