Stochastic Linear Model Predictive Control by Learning Uncertainty Using Gaussian Process Regression

Abstract

This paper proposes a method of model predictive control (MPC) based on Gaussian process regression for stochastic linear systems with uncertainty such as unknown dynamics and disturbances. The unknown dynamics refer to an unknown function of the input and output signals. In the proposed method, the mean and variance of the unknown function values estimate the function using Gaussian process regression. Updating the system model with the estimated function enhances the performance of MPC. Moreover, the stochastic reachable set of the system reduces the chance constraints into second-order cone constraints, which means the MPC problem becomes a convex problem. Finally, numerical examples illustrate the effectiveness of the proposed MPC.