Integrating Path Integral Control With Backstepping Control to Regulate Stochastic System

Abstract

Path integral control integrated with backstepping control is proposed to address the practical regulation problem, wherein the system dynamics are represented as stochastic differential equations. Path integral control requires the sampling of uncontrolled trajectories to calculate the optimal control input. However, the probability of generating a low-cost trajectory from uncontrolled dynamics is low. This implies that the path integral control requires an excessive number of trajectory samples to approximate the optimal control input appropriately. Therefore, we propose an integrated method of backstepping and path integral control to provide a systematic approach for sampling stabilized trajectories that are close to the optimal one. This proposed method requires a relatively small number of samples than that of the path integral control and uses the terminal set to further reduce the computational load. In simulation studies, the proposed method is applied to a single-input single-output example and a continuous stirred-tank reactor for demonstration. The results show the advantages of integrating the backstepping control and the path integral control.