Uncertainty quantification of model predictive control for nonlinear systems with parametric uncertainty using hybrid pseudo-spectral method

Abstract

In this paper, a hybrid pseudo-spectral (hPS) method is utilized to analyze the uncertainty of the model predictive control (MPC) for nonlinear systems with stochastic parameter uncertainty. The hPS method incorporates Generalized polynomial expansion (gPC) and pseudo-spectral (PS) optimal control in a hybrid format. To quantify the effect of uncertainty on the MPC states and control inputs, we use the gPC method, and for time discretization of the MPC problem, the pseudo-spectral method is employed. The proposed method will be compared with the well-known Monte Carlo (MC) simulation method in terms of computational speed. Two dynamical systems are tested. First, an industrial process, continuous stirred reactor tank, which is a highly nonlinear system, with Gaussian distributed parameter uncertainty and second, a typical second-order dynamical system with uniform and Weibull distributed parameter uncertainty. Simulation results demonstrate that the proposed method can approximate the two first moments of the states and control inputs under MPC much faster and computationally more efficient than MC simulations.

Keywords

• model predictive control
• uncertainty analysis
• generalized polynomial chaos
• pseudo-spectral optimal control