Prescribed-time fault-tolerant synchronization control of complex dynamical networks using time-varying protocols

This research delves into the intricacies of the prescribed-time synchronization control problem of a class of complex dynamical systems, all while factoring in the presence of time-varying actuator faults. An innovative time-varying protocol is initially established for the case of additive actuator faults, hinging on the solution to a particular set of parametric Lyapunov equations. Through the astute exploitation of the scalarization properties intrinsic to the solution to the parametric Lyapunov equation, the time-varying parameter within the protocol is effectively ascertained. Furthermore, to mitigate the impact stemming from multiplicative actuator fault(s), an alternative protocol is also introduced. Through rigorous analysis rooted in the principles of Lyapunov, it is demonstrated that the synchronization errors in both scenarios remain bounded, ultimately converging to zero within a predetermined time frame. The developed protocols are employed in coupled Chua's circuit control systems with faulty actuators, and simulation results validate the efficacy of the proposed approaches.