This paper derives a filtering and a smoothing algorithm for simultaneous input and state estimation for linear discrete-time systems of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">any</i> inherent delay. The exogenous input is assumed to be completely unknown and the only stochastic assumptions are on the output measurements and the initial state. The algorithm includes the Kalman filter which is itself a special case of a system with an inherent delay of zero. The derived recursions take a similar form to the Kalman filter, and are straightforward to implement. The approach uses a standard characterisation of a system's inherent delay in terms of the incremental ranks of a sequence of Toeplitz matrices of Markov parameters. Two judiciously chosen rank decompositions of the relevant Toeplitz matrix corresponding to the inherent delay are used to develop the algorithm. Conditions for the convergence of the filter are also derived and consist of a controllability condition and a minimum phase condition. The paper also presents a smoothing algorithm that can estimate the states and inputs of the system over a fixed time horizon. The theory is illustrated on a field controlled DC motor system with an inherent delay of two and a mass-spring-damper chain system with an inherent delay of five.

This paper addresses the security allocation problem in a networked control system under stealthy injection attacks. The networked system is comprised of interconnected subsystems which are represented by nodes in a digraph. An adversary compromises the system by injecting false data into several nodes with the aim of maximally disrupting the performance of the network while remaining stealthy to a defender. To minimize the impact of such stealthy attacks, the defender, with limited knowledge about attack policies and attack resources, allocates several sensors on nodes to impose the stealthiness constraint governing the attack policy. We provide an optimal security allocation algorithm to minimize the expected attack impact on the entire network. Furthermore, under a suitable local control design, the proposed security allocation algorithm can be executed in a scalable way. Finally, the obtained results are numerically validated through using Erdős-Rényi random graphs for generality.

Achieving leaderless asymptotic synchronization for uncertain multi-agent systems while guaranteeing prescribed transient performance remains a significant challenge for traditional methods. This difficulty arises from the redundancy between relative errors and performance functions in nonlinear dynamics, which obscures the explicit expression of local topological information in terms of the Laplacian matrix. In this work, we propose an adaptive asymptotic consensus control with unified prescribed performance for multi-agent systems, which exhibits several notable features. Firstly, we construct a homeomorphic function transformation for the relative error, enabling multiple prescribed performance behaviors to be maintained under a fixed control structure. Secondly, we establish a quantitative relationship between the transformed error and the relative error, revealing the lower bound of the transformed error-based normalized Jacobian, which is crucial for asymptotic control design. Thirdly, we introduce a robust decomposition technique in the developed lemma, allowing the redundancy to be split into two independent components. By incorporating a negative feedback element into the proposed controller and utilizing a parameter estimation technique, we further compensate the redundancies and guarantee the asymptotic stability of the closed-loop system. Simulation results illustrate the effectiveness of the proposed control scheme.

In this note, we address the stability problem for a class of hybrid systems, which contains continuous and logical dynamics. First, we introduce the so-called hybrid system in detail, and give the algebraic form of the system utilizing the semi-tensor product (STP, i.e., Cheng product) of matrices. Next, a new stability concept for the hybrid system is proposed by extending the definitions of set stability and exponential stability. After that, several stability criteria are presented by employing Lyapunov-like functions and STP. Accordingly, the stability conditions in some special cases are derived. Finally, the theoretical results are illustrated by some numerical examples.

A theorem is proved to verify incremental stability of a feedback system via a homotopy from a known incrementally stable system, making no assumptions on existence of an extended space, well-posedness or causality. A first corollary of that result is that incremental stability may be verified by separation of Scaled Relative Graphs, correcting two assumptions in [1, Theorem 2]. Necessity of this correction is demonstrated by example. A second corollary provides an incremental version of the classical IQC stability theorem. Finally it is shown how to relax assumptions of incremental boundeness on the operators.

This paper studies distributed Time-Varying Resource Allocation (TVRA) where the local cost functions, global equality constraints, and Local Feasibility Constraints (LFCs) vary with time. Algorithms that mimic the structure of feedback-feedforward control systems are proposed. Feedback and feedforward laws are generated using local estimates from a distributed estimator, while a distributed controller enforces the stationarity condition within a fixed time and updates the candidate solution accordingly. To handle the LFCs, feedback laws based on projection and feedforward laws that switch between different modes are introduced as an initialization-free alternative to the barrier-based methods used in most related works. Our projection-based method guarantees that, for any infeasible initial value, the state trajectory enters the locally feasible set within a fixed time and remains within it thereafter, and that the set is forward invariant if the initial value is locally feasible. Convergence analyses are conducted under mild assumptions. For cases without LFCs, the proposed algorithm converges to the optimal trajectory within a fixed time. For cases with LFCs, the proposed algorithm is globally asymptotically stable at the optimal trajectory while exhibiting fixed-time convergence between consecutive switching instants. Numerical examples and a power system application verify their effectiveness.

Control barrier function (CBF) safety filters emerged as a popular framework to certify and modify potentially unsafe control inputs, for example, provided by a reinforcement learning agent or a non-expert user. Typical CBF safety filter designs assume that the system has a uniform relative degree. This assumption is restrictive and is frequently overlooked in practice. When violated, the assumption can cause the safety filter to become inactive, allowing large and possibly unsafe control inputs to be applied to the system. In discrete-time implementations, the inactivity issue is often manifested as chattering close to the safety boundary and/or constraint violations. In this work, we provide an in-depth discussion on the safety filter inactivity issue, propose a mitigation strategy based on multiple CBFs, and derive an upper bound on the sampling time for safety under sampled-data control. The effectiveness of our proposed method is validated through both simulation and quadrotor experiments.

Opacity is a property of discrete event systems that allows to hide a secret from external observers. If the secret is the system initial state, then the related opacity problem is referred to as Initial State Opacity (ISO). The problem of ISO verification is usually approached at a logical level, by taking into account only the order of event occurrences. However, if the timing structure of the system is known, opacity analysis can be refined. This paper contributes to this line of research by proposing a result to assess opacity in a timed perspective. In such a framework, it is possible to establish how long the secret can be hidden from a malicious observer; indeed, by exploiting the timing information, the intruder may infer the secret, even if the system is logically opaque.