Adaptive Optimal Output Tracking Control of Completely Unknown Linear Two-Time-Scale Systems

In this note, the infinite horizon optimal output tracking control problem for two-time-scale systems is investigated. The problem is transformed into an optimal regulator problem of the augmented system which is constructed based on the command generator and the original system. The adaptive dynamics programming technique is utilized to learn the optimal solution in real time without relying on the knowledge of system dynamics. By the structured cost function parameter matrix for a full-order model, ill-conditioned numerical issue of two-time-scale systems is overcome. The proposed algorithm has a rigorous convergence proof. Finally, a DC system is given to show the feasibility of the proposed scheme by simulation.