A Numerical Algorithm for Self-Learning Model Predictive Control in Servo Systems

Abstract

Model predictive control (MPC) is one of the most effective methods of dealing with constrained control problems. Nevertheless, the uncertainty of the control system poses many problems in its performance optimization. For high-precision servo systems, friction is typically the main factor in uncertainty affecting the accuracy of the system. Our work focuses on stochastic systems with unknown parameters and proposes a model predictive control strategy with machine learning characteristics that utilizes pre-estimated information to reduce uncertainty. Within this model, the parameters are obtained using the estimator. The uncertainty caused by the parameter estimation error in the system is parameterized, serving as a learning control component to reduce future uncertainty. Then, the estimated parameters and the current state of the system are used to predict the future p-step state. The control sequence is calculated under the MPC’s rolling optimization mechanism. After the system output is obtained, the new parameter value at the next moment is re-estimated. Finally, MPC is carried out to realize the dual rolling optimization mechanism. In general, the proposed strategy optimizes the control objective while reducing the system uncertainty of the future parameter and achieving better system performance. Simulation results demonstrate the effectiveness of the algorithm.