Distributed time‐varying convex optimal consensus control for multi‐agent system with/without chattering restrain

Abstract

In this article, the consensus, collision avoidance, and distributed convex optimization problems of a class of multi-agent systems with a time-varying objective function are studied. Moreover, the proposed method in this article can reduce the chattering problem of the controller input caused by the sign function. First, the sign function is used to design the controller to improve the convergence rate of the system, on this basis, the optimization item is designed for the more complex time-varying objective function to ensure that the value of the objective function is the smallest when the system achieves the speed consensus. Second, considering the chattering problem caused by the sign function, the designed controller is improved to reduce the chattering phenomenon.Third, two novel Lyapunov functions are constructed to verify the stability of the system and the distributed optimization objective. Due to the controller is designed for the time-varying objective function, moreover, the tasks of the formation and collision avoidance are needed to take into account, therefore, the designed Lyapunov functions in this article are more difficult. Finally, the formation function is designed to ensure that the multi-agent system achieves the desired formation configuration. The simulation results show the correctness of the theoretical design of this article and the superiority in extending the running time of the system.

Observer‐based output feedback event‐triggered consensus tracking for linear multi‐agent systems

“…Theorem 1. Under Assumption 2, the DET UIO (4) combined with the triggering function (5) can estimate the relative state x i for i = 1, … , N, if there exist matrices Q and Λ > 0 such that the following LMI holds…”

“…Next, we will use the method by contradiction to prove that Zeno behavior is excluded. Suppose that the triggering function (5) ) .…”

“…In this paper, although the time sequences t i k and q i k are determined by different triggering conditions, ruling out Zeno behavior is no more complicated than in the cases of References 18-23 with a single triggering mechanism, since the updates of both are asynchronous. Furthermore, it can be seen that triggering function (19) is more general than triggering function (5). On the one hand, when 𝜉 i ≡ 0 and 𝜗 2 is chosen as an exponential function, the DET mechanism is transformed into the EET mechanism.…”

“…Whether the consensus can be achieved is one of the fundamental problems in MASs. [5][6][7][8] Its purpose is to make the states or outputs of the system tend to an agreement on certain quantities by designing appropriate distributed control strategies. In general, the consensus control of MASs can be roughly categorized into two classes, namely, leaderless consensus and leader-follower consensus.…”

“…Therefore, the cooperative control of MASs has gained more and more attention from many fields. Whether the consensus can be achieved is one of the fundamental problems in MASs 5–8 . Its purpose is to make the states or outputs of the system tend to an agreement on certain quantities by designing appropriate distributed control strategies.…”