Optimal Trajectory Tracking for Unknown H∞ Constrained Systems Based on Reinforcement Learning

This letter obtains a solution for the optimal trajectory tracking of unknown H∞)-constrained systems using reinforcement learning to derive the Nash equilibrium. To illustrate the H∞) tracking, a discounted performance function with multi-inputs in
$L$
2
-gain is provided. An augmented vector, consisting of known bounded reference trajectory and tracking error, is constructed to describe the augmented system. Along the augmented system, a new index function is introduced to formulate the optimal tracking control problem. This letter presents a policy iteration algorithm that provides the Nash equilibrium solution, even without the system dynamics information. By applying Pontryagin's maximum principle and introducing a novel costate, the system's stability is ensured through the determination of its upper bound. Thorough examination verifies that the suggested tracking algorithm converges effectively when using the Hamilton-Jacobi-Isaacs (HJI) equation.