Optimal Control of Nonlinear System With Input Delay via Policy Iteration Algorithm

ABSTRACT This article proposes a method that combines equivalent system transformation with adaptive dynamic programming (ADP) for the nonlinear system with input time‐delay. Firstly, the paper introduces a delay compensation method to convert the time‐delayed system into a delay‐free equivalent. This approach effectively mitigates the impact of the delay term on the control performance. Secondly, the transformed model facilitates the derivation of optimal control input. Then, the policy iteration (PI) algorithm is employed in approximating the optimal control through alternating execution of two core steps: one is policy evaluation, and the other is policy improvement. Lyapunov stability theory is applied to conduct a rigorous stability analysis of a nonlinear system with input delay. Additionally, neural networks are applied for online approximation. By analyzing the weight update process of the neural network, the asymptotic convergence and ultimate uniform boundedness of the weight errors are proven. Finally, simulation results further validate the feasibility of the described framework.