This paper investigates fixed-time interval state estimation (F-ISE) methods for perturbed continuous- and discrete-time linear systems. A novel delay injection-based non-smooth F-ISE structure is proposed, using computed bounds on the piecewise observation error. The existence conditions of this F-ISE structure are formulated as constrained matrix equations (MEs) that impose no additional requirements on the system matrix, fixed-time constant, or measurement noise. By solving these MEs, a parametric feasible solution for the F-ISE is obtained under a common observability condition, providing explicit design degrees of freedom for further component-wise optimization. Additionally, we present a detailed discussion on the relationship between the proposed method and the extensions of this non-smooth structure in comparison with other existing ISE methods. Finally, two comparative simulations demonstrate the advantages of the proposed approach over existing methods.
This paper investigates the problem of data-driven distributed moving horizon estimation for unknown linear discrete-time systems using pre-collected data and inaccurate prior system models. First, we construct a distributed system representation by fusing data and prior models from different sensors. Based on this representation, we develop a novel data-driven distributed moving horizon estimator. We then conduct a performance analysis, and propose a parameter design method to ensure the stability of the proposed estimator. Recognizing that the estimator’s performance is highly dependent on the accuracy of the identified system parameters. We further establish a quantitative relation between the parameter estimation accuracy and both the sample number and the accuracy of the prior models. Finally, a target tracking example is presented to demonstrate the effectiveness of the proposed algorithm.
This paper considers the quickest detection problem for general dependent processes in a Bayesian setting. This paper establishes that Shiryaev’s rule, a simple threshold test on the no-change posterior, is an exactly optimal solution in the general dependent setting when the change time prior distribution is geometric. The presented analysis approach provides insights into the necessity and sufficiency of the change time prior distribution assumption and highlights how the nature of optimal solutions will change under assumption relaxation. This paper also establishes that strong duality holds when measurements have continuous conditional distributions. Finally, a novel, computationally efficient, relaxed-dependence test statistic is proposed which is shown to be weakly convergent to Shiryaev’s test statistic.
We present a tractable safe control framework, referred to as discrete Control Barrier Proximal Dynamics (D-CBPD), for a class of quantized multi-actuator and sampled-data systems. We first characterize the tracking behavior of discretized parametric contracting dynamics. Next, we analyze discrete contracting dynamics as controllers and establish bounds on system evolution, shown to be linear for non-expansive systems. These bounds are then translated into control deviations at sampling instants and during inter-sample evolution using one-sided Lipschitz properties. Building on this, we introduce D-CBPD, which tracks the solution of a CBF-based QP controller, ensuring continuous safety with a bounded, tunable violation margin. We further propose discretization as a recurrent triggering mechanism for a generalizable approach to safe quantized control. The method is validated through simulations for thermal management of an air-cooled lithium-ion battery pack with multiple cooling fans, demonstrating its effectiveness in ensuring safety while remaining computationally scalable.
In this paper, we revisit average consensus problems for undirected networks of agents subject to communication delays and switching topologies within the framework of partial difference equations over graphs. Focusing on integrator-type agents, we primarily study tight estimates of the maximal tolerable delay for an observer-type protocol. This protocol, a variant of the delayed Laplacian, is designed to enhance disturbance rejection. Uniform/nonuniform delays associated with static/switching topologies are handled in a unified framework. The main results provide scalable and computationally simple sufficient conditions for average consensus, which are also shown to be necessary in certain cases. Compared to the state of the art, the proposed method not only recovers known delay upper bounds but also achieves tighter bounds in several scenarios.
It is well known that Zakai equation in the nonlinear filtering (NLF) governs the evolution of unnormalized density function of the states conditioned on the observation history. In this paper, the NLF is investigated in a jump-diffusive Lévy stochastic system where the state space model is based on heavy-tailed non-Gaussian α-stable Lévy process, and the observations are driven by mutually independent jump and diffusion processes. In order to deal with the NLF problem efficiently, we approximate its corresponding Zakai equation by splitting it up into two stochastic processes on discretized time intervals, which actually correspond to the prediction and updating steps, respectively, in the NLF setting. The main contribution of this paper is that theoretically the strong and weak convergence results of splitting-up Zakai equation are generalized to the NLF models with non-Gaussian α-stable Lévy states and mixed type observations. To demonstrate our theoretical analysis, correspondingly, we extend the Yau-Yau algorithm, originally proposed by the classical NLF problems under Gaussian noises to the heavy-tailed non-Gaussian α-stable Lévy process. Furthermore, the performance of our proposed algorithm is illustrated by presenting some challenging example of highly nonlinear tracking cubic sensor. The experimental results indicate that the proposed filtering algorithm yields much more efficient and accurate performance, vastly superior than that of the sequential importance resampling (SIR) particle filter.
This paper focuses on investigating the adaptive tracking problem for a kind of nonsmooth nonlinear systems subject to full-state constraints. Through the utilization of carefully designed auxiliary signals, the challenge posed by full-state constraints is reduced to a constraint problem for two composite variables. This transformation enables the direct proposal of the controller without involving recursive procedures. Consequently, the conventional backstepping method is unnecessary, subsequently effectively mitigating the issues of complexity explosion and feasibility condition. These problems are inherent within the traditional backstepping framework, typically arising from the necessity for repeated differentiation and explicit upper bounds of virtual controllers, respectively. The stability of the closed-loop system and the asymptotic convergence of the tracking error are all proven by strict analysis. Finally, the proposed control method is applied to a crane system, and the control effectiveness is verified through experiment results.
This paper introduces a dual superlevel sets framework for affine nonlinear systems with high-relative-degree outputs and safety-critical constraints, where output tracking (treated as soft constraints) and safety enforcement (treated as hard constraints) are unified via hierarchical control barrier functions (CBFs). By constructing cascaded high-order derivative sets initialized from these super-level sets, convergence and safety conditions are rigorously established. To circumvent the computational complexity of traditional high-order CBF methods, an online Lyapunov-like condition solver is first proposed by exploiting the Faà-di-Bruno’s formula, which explicitly encodes high-order derivative constraints (up to the system relative degree) into a real-time quadratic programming (QP) problem. The resulting QP problem incorporates n-th-order Lie derivatives of safety and output constraints as algebraic conditions, while controller feasibility is ensured through the introduction of a slack variable. Finally, the effectiveness of the proposed method is demonstrated through single-link manipulator.
This paper is concerned with the adaptive model reference tracking control problem for 2 × 2 hyperbolic partial differential equations (PDEs) under event-triggered control. We consider the scenario where the control is applied only when necessary, as determined by a dynamic event-triggering condition. The aim is to conserve the computational and communication resources relevant to control. The event-triggered adaptive control is presented by emulation, and an even-triggering condition is proposed to determine the time instants when the control input should be updated. Under the event-triggered mechanism, a minimal dwell-time is guaranteed between consecutive triggering time instants, and the measured signal is ensured to asymptotically track the output of the reference model. Finally, the obtained results are used for an numerical example to validate the effectiveness of the event-triggered control method.
This paper studies wireless energy theft and Denial-of-Service (DoS) jamming on remote state estimation. The sensor charged by an energy harvester with Wireless Power Transfer (WPT) runs a Kalman filter and transmits its local estimate to a remote estimator. A threat actor (TA) is considered which can either conduct DoS jamming attack or steal wireless charging energy at each time instant. It aims to find an online policy to maximize the expected average sum of the energy gains and the remote estimation error. To address this sequential decision-making problem, we formulate it as a Markov decision process (MDP). We first establish the existence of an optimal deterministic Markov stationary policy. Moreover, we prove that this optimal policy has a nice threshold structure, which can significantly reduce computational costs. As the closed-form of optimal policy cannot be obtained, two approximation methods are proposed to seek a near-optimal policy. Finally, a numerical example is used to verify the theoretical results.
Multi-agent systems (MASs) exchange information through the network topology, which is prone to denial-of-service (DoS) attacks and detection delays. DoS attacks can interrupt communication channels, and detection delays may lead to asynchronization between the network topology and the controller, thereby making cooperative output regulation difficult to achieve. Thus, it is important to study the cooperative output regulation problem under DoS attacks and detection delays. This paper investigates the asynchronous resilient cooperative output regulation problem for uncertain nonlinear MASs subject to DoS attacks and detection delays. Asynchronous resilient distributed observers are proposed to estimate the exosystem’s matrix and state information, respectively. Based on the designed distributed observers, an asynchronous resilient cooperative output regulation control strategy is developed by using the backstepping control technique. The proposed control strategy is able to guarantee that the regulation errors converge asymptotically to zero even under DoS attacks and detection delays. Finally, a numerical example is given to check the effectiveness of the proposed observers and control strategy.
Most existing studies on containment control with position constraints rely on the properties of convex sets, with little attention given to non-convex constraints. In this paper, we consider a special class of non-convex constraint sets, star convex sets, regions that contain a point from which every boundary point is visible. Unlike the usual convex setting, which typically assumes that the intersection of all followers’ constraint sets is nonempty and contains the leader convex hull, we investigate the achievability of containment control even when followers’ constraint sets do not overlap. To address this challenge, we first propose a projection-based control algorithm and explore the conditions relating followers’ constraint sets and the convex hull formed by leaders. We then reformulate the update equation and establish an inequality that bounds each follower’s distance to the convex hull, and we analyze the asymptotic behavior of followers in three representative scenarios. By recursively examining the convergence of each follower, we show that containment is successfully achieved while ensuring all followers remain within their respective star-convex sets, provided that the union of communication graphs contains a directed path from the leaders to every follower. Finally, simulation results are presented to validate our theoretical findings.
