A new weight selection algorithm using SPSA for model predictive control

Abstract

Model Predictive Control (MPC) is one of the control methods for discrete time systems. The optimal input is calculated by using Linear Quadratic Regulator (LQR). The weight matrices in the evaluation function for LQR are determined by a designer with professional experience and a trial & error approach. Therefore, even if the same system is targeted, the performance can differ depending on the designer. This paper proposes a new weight selection algorithm using Simultaneous Perturbation Stochastic Approximation (SPSA) for MPC. A new evaluation function is proposed for the selection algorithm. Numerical values of the overshoot and the settling time are directly applied as the user’s requirements in this evaluation function. The optimal weight matrices numerically satisfying those requirements can be selected by the proposed algorithm. Simulation study of a zero momentum spacecraft shows that the proposed method is effective for the weight selection with consideration of performance.

Keywords

• model predictive control
• weight selection
• simultaneous perturbation stochastic approximation
• overshoot
• settling time