A novel model predictive controller for uncertain constrained systems

Model Predictive Control (MPC) is a method of choice for control of many industrial applications. MPC uses optimization based prediction of a model in a predetermined horizon to determine control action. While uncertainty is an inherent part of most dynamical systems, model mismatches in the case of uncertain dynamical system lead to undesirable closed loop response from steady state errors to instability. There are several research studies for robust MPC. However, most of the results are very conservative, where optimality is sacrificed to obtain worst case constraint satisfaction. This paper presents a novel MPC for control of non-linear uncertain dynamical systems with reliability type constraints, where the probability of violation of constraints is limited. We utilize polynomial chaos expansion (PCE) in order to propagate uncertainties. We show that it is possible to transform probabilistic constraints to a deterministic constraint on PCE coefficients. This approach prevents sampling of the uncertainty, thus it is efficient numerically and computationally.