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Resilient tracking consensus over dynamic random graphs: A linear system approach

EUROPEAN JOURNAL OF APPLIED MATHEMATICS 2023年第2期34卷 408-423页

作者： Shang, Y. Northumbria Univ Dept Comp & Informat Sci Newcastle Upon Tyne NE1 8ST Tyne & Wear England

Cooperative coordination in multi-agent systems has been a topic of interest in networked control theory in recent years. In contrast to cooperative agents, Byzantine agents in a network are capable to manipulate their data arbitrarily and send bad messages to neighbors, causing serious network security issues. This paper is concerned with resilient tracking consensus over a time-varying random directed graph, which consists of cooperative agents, Byzantine agents and a single leader. The objective of resilient tracking consensus is the convergence of cooperative agents to the leader in the presence of those deleterious Byzantine agents. We assume that the number and identity of the Byzantine agents are not known to cooperative agents, and the communication edges in the graph are dynamically randomly evolving. Based upon linear system analysis and a martingale convergence theorem, we design a linear discrete-time protocol to ensure tracking consensus almost surely in a purely distributed manner. Some numerical examples are provided to verify our theoretical results.

关键词： linear systems in control theory graphs and linear algebra random graphs controllability

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Discontinuous control in problem of disturbance reduction for a linear dynamical system

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MATHEMATICAL METHODS IN THE APPLIED SCIENCES 2023年第0期

作者： Maksimov, Vyacheslav I. I. Russian Acad Sci Krasovskii Inst Math & Mech Ural Branch 16 S Kovalevskaya Str Ekaterinburg 620990 Russia

In the paper, we study the problem of active reduction of the influence of a disturbance on the output of a linear controlled system. The problem is investigated on infinite time intervals. We consider a system of linear differential equations under the action of an unknown disturbance and a control to be formed. Our goal is to design an algorithm for reducing the disturbance by means of an appropriate control on the basis of inaccurate measurements of all (or a part of) phase coordinates of the system. This algorithm should form a feedback control that would guarantee that the trajectory of the given system and the velocity of its changing track the trajectory and the velocity of its changing of some reference system. We present two algorithms for solving this problem. These algorithms forming piece-wise constant controls are based on the combination of constructions of the theory of dynamical inversion and the theory of feedback control. They are stable with respect to informational noises and computational errors.

关键词： feedback control linear systems in control theory

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