Separation Principle for Event-Triggered Prescribed-Time Consensus Tracking of Nonlinear Multi-Agent Systems under DoS Attacks

Abstract

Despite the recent development of control theory for multi-agent systems (MASs), the highly desirable separation principle is difficult to establish even for linear MASs, let alone for nonlinear ones that rely solely on output measurements under denial-of-service (DoS) attacks. This paper establishes a separation principle for distributed leader-following control of this class of nonlinear MASs, allowing the observer and the controller to be designed independently. For each agent, two parametric Lyapunov equations (PLEs) are employed to generate two symmetric positive-definite matrices, which respectively support the independent design of the controller gain and the observer gain. To ensure that these two parameters do not affect each other, we adopt a matrix pencil formulation to decouple the relevant coupled terms and exploit time-varying feedback to handle potential impacts arising from nonlinearities. Furthermore, we design a hybrid observer that consists of a local state observer for reconstructing unmeasurable follower states and a distributed leader state observer for estimating the inaccessible leader state. Notably, we find that as long as the nonlinearity of all agents satisfies a linear-growth-type condition and the nonlinear model of the leader is available for followers, the separation principle can be established regardless of the presence of event-triggered control and/or admissible DoS attacks. In our method, the selection of design parameters for each agent is elegantly simple, involving only three parameters: one for the prescribed convergence time $t_f$, and the other two for the controller and the hybrid observer, respectively. Moreover, the latter two parameters can be chosen independently from explicit admissible ranges once the system order is specified. Numerical simulations verify the effectiveness of the proposed method.