Anti-attack compensator-based observer for adaptive prescribed-time bipartite consensus tracking control of nonlinear MASs under DoS attacks

This paper presents an adaptive prescribed-time bipartite consensus tracking control (PBCTC) scheme for nonlinear multi-agent systems (MASs) with denial-of-service (DoS) attacks by designing an improved anti-attack compensator-based (AACB) observer. Since the output signals and the states of the studied systems are unavailable in the presence of intermittent DoS attacks, we design the AACB observer to compensate for the output signals and reconstruct the system states. Furthermore, we formulate a sigmoid-based continuous DoS attack model with an attack duration parameter, which prevents large overshoots caused by the discontinuous input signals of the AACB observer. By introducing a time-varying constraint function in the backstepping design process, a new adaptive prescribed-time controller is constructed such that the prescribed-time tracking control problem under consideration is converted into the constraint problem of the tracking errors. Based on the Lyapunov stability theory and an auxiliary variable, the proposed time-triggered and event-triggered adaptive security control strategies can ensure that the bipartite consensus tracking errors converge to the pre-set region in the predefined time and the whole signals remain bounded in an insecure network environment. Finally, simulation results on pendulum systems are provided to illustrate the effectiveness of the developed control method.