Search

In this article, an output‐feedback Q‐learning algorithm is proposed for the discrete‐time linear system to deal with the H∞$$ {H}_{\infty } $$ tracking control problem. The problem is formulated as a zero‐sum game in the Stackelberg game framework with a discount factor to make the value function bounded. According to the principle of optimality, the game algebraic Riccati equation (GARE) is derived and solved by the Q‐learning algorithm to get the optimal solution of the Stackelberg game without requiring the knowledge of system dynamics and state. It is proved that the solution of the algorithm converges to the optimal control input and the worst‐case disturbance with excitation noises during training, and the Stackelberg strategy can achieve a lower L2$$ {L}_2 $$ disturbance attenuation level than the Nash one. Moreover, the impacts of the discount factor on the stability of the closed‐loop system and solvability of the GARE are analyzed to provide some criteria for the choice of the discount factor. Simulation examples are provided to validate the effectiveness of the algorithm. [ABSTRACT FROM AUTHOR]

Summary: In this paper, we propose a model‐free algorithm for global stabilization of linear systems subject to actuator saturation. The idea of gain‐scheduled low gain feedback is applied to develop control laws that avoid saturation and achieve global stabilization. To design these control laws, we employ the framework of parameterized algebraic Riccati equations (AREs). Reinforcement learning techniques are developed to find the solution of the parameterized ARE without requiring any knowledge of the system dynamics. In particular, we present an iterative Q‐learning scheme that searches for a low gain parameter and iteratively solves the parameterized ARE using the Bellman equation. Both state feedback and output feedback algorithms are developed. It is shown that the proposed scheme achieves model‐free global stabilization under bounded controls and convergence to the optimal solution of the ARE is achieved. Simulation results are presented that confirm the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]