Resilient ${H_\infty }$ Control for Nonlinear Systems with Uncertainties and Disturbances Based on Equivalence Robust Passivity

It is always a challenge to design a resilient controller for nonlinear engineering systems, particularly for a system with external disturbance, uncertainties, and high couplings. This paper systematically investigates the stability issues on complex resilient nonlinear systems with various disturbances and uncertainties. Initially, to address the difficulty in solving differential Hamilton-Jacobi inequalities, a resilient anti-disturbance controller is designed by using the robust passive theory to guarantee that the closed-loop nonlinear system is asymptotically stable with ${H_\infty }$ property. To obtain the conventional design of the storage function, the equivalent robust passive system is introduced through a global diffeomorphism, and the corresponding stability analysis is conducted to verify the effectiveness of the method. The simulation results for a helicopter system are intended to demonstrate the practicality and validity of the proposed control method in solving nonlinear resilient control problems.