Polynomial chaos explicit solution of the optimal control problem in Model Predictive Control

A difficulty still hindering the widespread application of Model Predictive Control (MPC) methodologies, remains the computational burden that is related to solving the associated Optimal Control (OC) problem for every control period. In contrast to numerous approximation techniques that pursue acceleration of the online optimization procedure, relatively few work has been devoted towards shifting the optimization effort to a precomputational phase, especially for nonlinear system dynamics. Recently, interest revived in the theory of general Polynomial Chaos (gPC) in order to appraise the influence of variable parameters on dynamic system behaviour and proved to yield reliable results. This article establishes an explicit solution of the multi-parametric Nonlinear Problem (mp-NLP) based on the theoretical framework of gPC, which enabled a polynomial approximated nonlinear feedback law formulation. This resulted in real-time computations allowing for real-time MPC, with corresponding control frequencies up to 2 kHz,