Integral Reinforcement Learning for Tracking in a Class of Partially Unknown Linear Systems With Output Constraints and External Disturbances

Abstract

In this paper, the $H_\infty $ tracking control problem of partially unknown linear systems with output constraints and disturbance is studied by the reinforcement learning (RL) method. Firstly, an augmented system is established based on the reference trajectory dynamics and target system dynamics, and a special cost function is established to realize asymptotic tracking. In addition, the barrier function (BF) is used to transform the augmented system, and the output constraints is realized simultaneously by minimizing the quadratic cost function of the transformed system. Using only the obtained data and part of the system dynamics, the optimal control strategy and the worst disturbance strategy are obtained by using the integral reinforcement learning (IRL). Rigorous stability analysis shows that the proposed method can make the trajectory of system states converge, and the output of the control strategy can make the tracking error asymptotically stable. Finally, a simulation example is conducted to verify the effectiveness of the proposed algorithm.

Keywords

• Barrier function
• H∞ tracking control%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> <italic xmlns:ali="http://www.niso.org/schemas/ali/1.0/" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">H</italic>∞ tracking control
• integral reinforcement learning
• output constraints