Finite-time consensus protocols for multi-dimensional multi-agent systems
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RESEARCH ARTICLE
Finite-time consensus protocols for multi-dimensional multi-agent systems Jieqiang Wei1 · Bart Besselink2 · Junfeng Wu3 · Henrik Sandberg4 · Karl H. Johansson4 Received: 11 September 2020 / Revised: 18 September 2020 / Accepted: 29 September 2020 © South China University of Technology, Academy of Mathematics and Systems Science, CAS and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract A finite-time consensus protocol is proposed for multi-dimensional multi-agent systems, using direction-preserving signum controls. Filippov solutions and nonsmooth analysis techniques are adopted to handle discontinuities. Sufficient and necessary conditions are provided to guarantee infinite-time convergence and boundedness of the solutions. It turns out that the number of agents which have continuous control law plays an essential role in finite-time convergence. In addition, it is shown that the unit balls introduced by 𝓁p norms, where p ∈ [1, ∞] , are invariant for the closed loop. Keywords Multi-agent systems · Network consensus · Finite-time convergence · Nonsmooth analysis
1 Introduction Multi-agent systems (MAS) have a broad spectrum of applications in both military and civilian environments and have been a hot area of research for decades. The essential goal of the control of multi-agent systems is to let the agents achieve some states cooperatively with only local information exchange, e.g., [1, 2]. Among the vast applications of * Jieqiang Wei [email protected] Bart Besselink [email protected] Junfeng Wu [email protected] Henrik Sandberg [email protected] Karl H. Johansson [email protected] 1
Ericsson Global AI Accelerator, Torshamnsgatan 21, Stockholm, Sweden
2
Bernoulli Institute for Mathematics, Computer Science and Artificial Intelligence, University of Groningen, P.O. Box 407, 9700 Groningen, AK, The Netherlands
3
College of Control Science and Engineering, Zhejiang University, 310027 Hangzhou, China
4
Division of Decision and Control Systems, KTH Royal Institute of Technology, 10044 Stockholm, Sweden
MAS, the consensus problem, where the primary objective is to drive agent states to an agreement, is a benchmark problem [3]. The current paper considers finite-time consensus protocols which, first, have the advantage of providing a guarantee on the time it takes to reach consensus and, second, provide better robustness and disturbance rejection properties than the asymptotic case [4]. Existing results on finite-time consensus can roughly be divided into two groups: namely those exploiting continuous or discontinuous control protocols. These groups have in common that the nonlinear control laws are not Lipschitz continuous at the desired consensus space. For example, continuous strategies are usually based on applying a nonlinear state feedback strategy that includes fractional powers, e.g., [5–8], or on a high gain converging to infinity as time approaches the converging time, e.g., [9]. The discontinuous strategies utilize nonsmooth control tools, e.g., [10–16], typic
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