  This paper studies the adaptive optimal control problem for a class of linear
time-delay systems described by delay differential equations (DDEs). A crucial
strategy is to take advantage of recent developments in reinforcement learning
and adaptive dynamic programming and develop novel methods to learn adaptive
optimal controllers from finite samples of input and state data. In this paper,
the data-driven policy iteration (PI) is proposed to solve the
infinite-dimensional algebraic Riccati equation (ARE) iteratively in the
absence of exact model knowledge. Interestingly, the proposed recursive PI
algorithm is new in the present context of continuous-time time-delay systems,
even when the model knowledge is assumed known. The efficacy of the proposed
learning-based control methods is validated by means of practical applications
arising from metal cutting and autonomous driving.
