Learning Adaptive Optimal Controllers for Linear Time-Delay Systems *

This paper studies the learning-based optimal control for a class of infinite-dimensional linear time-delay systems. The aim is to fill the gap of adaptive dynamic programming (ADP) where adaptive optimal control of infinite-dimensional systems is not addressed. A key strategy is to combine the classical model-based linear quadratic (LQ) optimal control of time-delay systems with the state-of-art reinforcement learning (RL) technique. Both the model-based and data-driven policy iteration (PI) approaches are proposed to solve the corresponding algebraic Riccati equation (ARE) with guaranteed convergence. The proposed PI algorithm can be considered as a generalization of ADP to infinite-dimensional time-delay systems. The efficiency of the proposed algorithm is demonstrated by the practical application arising from autonomous driving in mixed traffic environments, where human drivers’ reaction delay is considered.