Model Predictive Control of Linear Parameter-Varying Systems Using Gaussian Processes

Linear parameter-varying (LPV) modeling is a powerful framework for representing time-varying systems as well as nonlinear dynamics in terms of a linear structure dependent on a time-varying parameter known as the scheduling parameter. Combining model predictive control (MPC) with LPV predictors (LPVMPC) results in an efficient parameter-dependent MPC approach. However, the future trajectory of the scheduling parameter required for formulating the LPVMPC optimization problem is not known in advance. In this paper, a Bayesian nonparametric approach within Gaussian process (GP) regression framework is introduced to predict the future behavior of the scheduling parameter over the MPC prediction horizon, which can be exploited by the proposed LPVMPC approach. The performance of the presented approach, i.e., GP-LPVMPC, is tested on a simulation example, where it is demonstrated that it outperforms the LPVMPC when the scheduling variable is frozen over the MPC prediction horizon in terms of convergence and control performance.