Cross-Scale Imperfect Data-Based Composite H ∞ $$ {H}_{\infty } $$ Control of Nonlinear Two-Time-Scale Systems

Abstract

Utilizing the cross-scale imperfect data, the reinforcement learning (RL) composite $H_{\infty }$ control of nonlinear two-time-scale (TTS) systems is proposed in the presence of unknown slow dynamics. First, with the feat of singular perturbation theory (SPT), the original $H_{\infty }$ control problem is decomposed and rearranged into standard fast and slow subproblems that have no cross terms between state, control and disturbance in the performance indices. Then, since the states of decomposed fast and slow subsystems cannot be measured perfectly, the state reconstruction mechanism is proposed based on the input-state data of the original system, and cross-scale information interaction is incorporated to correct the bias induced by the time-scale decomposition. Cross-scale composite RL algorithm is proposed with the $H_{\infty }$ slow and fast controllers designed in separate time scales. Next, the stability and $H_{\infty }$ performance of the TTS systems under the composite controller is analyzed considering the data inaccuracy of state reconstruction. Finally, the effectiveness of the proposed method is validated in the control application to the permanent magnet synchronous motor (PMSM) system.