On resilient strategy design of multi-tasking optimal control for state-saturated systems with nonlinear disturbances: The time-varying case

This paper is concerned with the resilient strategy design of the multi-tasking optimal control problem for a class of time-varying state-saturated systems. The system under investigation is subject to nonlinear disturbances and state saturations. In the context of noncooperative game, the resilient strategies are designed which can tolerate gain perturbations/variations resulting possibly from computational or implementation errors. First, an upper bound is derived on the individual cost function of each controller. Then, such an upper bound is minimized unilaterally via iteratively solving a convex optimization problem and, subsequently, the resilient control strategies are obtained in terms of the solutions to certain coupled backward Riccati-like recursions. Furthermore, the explicit expression for the derived upper bound is provided over the infinite horizon. Finally, a numerical example is exploited to demonstrate the validity of the proposed methodology.