Robust Optimal Tracking Control for Linear Systems via Adaptive Dynamic Programming method

This paper takes two-player systems as an example to study the robust optimal tracking control problem for linear discrete-time (DT) multi-player systems with constant uncertainty. To this end, by using adaptive dynamic programming (ADP) method and game theory, the optimal feedback control problem of the dynamic aspect was translated into a two-player cooperative game problem. Thus, we developed a novel off-policy cooperative game Q-learning algorithm first to learn the feedback controllers through the measured data along the system trajectories. Then the steady-state control inputs can be obtained by utilizing the Lagrange equation and correlative parameters learned from the proposed algorithm. Finally, the control inputs of the linear DT systems with uncertainty can be calculated by combining the feedback controllers and the steady-state control inputs. Simulation results are given to verify the effectiveness of the proposed method.