Data-Driven Adaptive Optimal Tracking Control for Completely Unknown Systems

In this paper, an online data-driven based solution is developed for linear quadratic tracking (LQT) problem of linear systems with completely unknown dynamics. By applying the vectorization operator and Kronecker product, an adaptive identifier is first built to identify the unknown system dynamics, where a new adaptive law with guaranteed convergence is proposed. By using system augmentation method and introducing a discounted factor in the cost function, a compact form of LQT formulation is proposed, where the feedforward and feedback control actions can be obtained simultaneously. Finally, a new policy iteration is introduced to solve the derived augmented algebraic Riccati equation (ARE). Simulation results are presented to demonstrate the effectiveness of the proposed algorithm.