Distributed resilient optimization control for uncertain nonlinear MASs under DoS attacks

In this paper, we consider the distributed optimization control problem for second-order uncertain nonlinear multi-agent systems (MASs) under denial-of-service (DoS) attacks. To solve the problem, a hierarchical control method consisting of designing a time-varying weight regulator in the signal processing layer, distributed resilient coordinators in the network communication layer, and decentralized resilient optimal controllers in the local control layer is proposed. Specifically, a time-varying weight regulator is first designed by using the polynomial interpolation method to ensure that the signal used from neighbors is continuously differentiable. Based on this weight regulator, distributed resilient coordinators with up to second-order derivatives are designed to generate a local reference signal for each agent to follow. Then, decentralized resilient optimal controllers are proposed by using the backstepping method. It is shown that the practical distributed optimization objective can be achieved by means of the developed method. Finally, a simulation example is provided to show the effectiveness of the proposed distributed resilient optimization method.