Reinforcement Learning Reduced H ∞ Output Tracking Control of Nonlinear Two-Time-Scale Industrial Systems

In this article, based upon reinforcement learning (RL) and reduced control techniques, an <tex-math notation="LaTeX">H∞</tex-math> output tracking control method is represented for nonlinear two-time-scale industrial systems with external disturbances and unknown dynamics. First, the original <tex-math notation="LaTeX">H∞</tex-math> output tracking problem is transformed into a reduced problem of the augmented error system. Based on zero-sum game idea, the Nash equilibrium solution is given and the tracking Hamilton–Jacobi–Isaacs (HJI) equation is established. Then, to handle the issue of unmeasurable states of the virtual reduced system, full-order system state data are collected to reconstruct the reduced system states, and the model-free RL algorithm is proposed to solve the tracking HJI equation. Next, the algorithm implementation is given under the actor–critic–disturbance framework. It is proved that the control policy obtained from reconstructed state data can make the augmented error system asymptotically stable and satisfy the L <tex-math notation="LaTeX">₂</tex-math> gain condition. Finally, the effectiveness of the proposed method is illustrated by the permanent-magnet synchronous motor experiment.