Event-Triggered Robust Optimal Control for Nonlinear Systems With Uncertain Dynamics and Nonzero-equilibrium

This paper proposes a robust optimal control strategy for a class of continuous-time nonlinear systems with dynamic uncertainties and nonzero equilibrium points. In existing robust optimal control designs, it is always assumed that the controlled system has a zero equilibrium, which cannot always be satisfied in practice. To overcome these limitations, a novel cost function is designed with respect to the state and its derivative, and an unknown disturbance bound, and then a robust optimal control problem is formulated for a nominal system. To solve this optimization, an event-triggered adaptive dynamic programming (ADP) is established to obtain the approximate optimal solution while saving computational resources. Furthermore, to eliminate the initial stable control condition, an auxiliary term is introduced into the classical gradient descent algorithm to update the weight parameters of the neural networks (NNs). The stability analysis shows that the system states and the approximation errors of the NNs are all uniformly ultimately bounded (UUB). Finally, simulation results demonstrate the validity of the proposed robust optimal control methods.