Nonlinear stochastic model predictive control via regularized polynomial chaos expansions

A new method to control stochastic systems in the presence of input and state constraints is presented. The method exploits a particular receding horizon algorithm, coupled with Polynomial Chaos Expansions (PCEs). It is shown that the proposed approach achieves closed loop convergence and satisfaction of state constraints in expectation. Moreover, a non-intrusive method to compute the PCEs´ coefficients is proposed, exploiting ℓ₂-norm regularization with a particular choice of weighting matrices. The method requires low computational effort, and it can be applied to general nonlinear systems without the need to manipulate the model. The approach is tested on a nonlinear electric circuit example.