Triggering and Control Co-design of Nonlinear Systems with External Disturbances Using Adaptive Dynamic Programming

This paper proposes a joint optimization strategy for nonlinear systems subject to unknown external disturbances. The co-design problem is formulated as a two-player zero-sum game, where the control policy is treated as the first player and the control input error caused by aperiodic feedback is treated as the second player. Besides, a robust term is incorporated to the performance index to suppress the negative effect of external disturbances. Based on the game theory, the optimal performance index and the solution to the associated Hamilton-Jacobi-Isaacs (HJI) equation can be obtained. Then, the sampling intervals are optimized by designing an event-triggered condition according to Lyapunov direct method. Furthermore, a self-triggered strategy is introduced to predict the next triggering instant in advance, avoiding the requirement of continuous state measurements. Through critic-only neural network (NN) implementation, the event-based HJI equation is approximated by using adaptive dynamic programming technique. The closed-loop nonlinear system and the weight estimation error for the critic NN are both guaranteed to be uniformly ultimately bounded under the proposed aperiodic sampling mechanism. Finally, simulation results and comparison studies demonstrate the effectiveness of the proposed co-design approach.