Stochastic nonlinear predictive controller and method based on uncertainty propagation by gaussian-assumed density filters

Abstract

Stochastic nonlinear model predictive control (SNMPC) allows to directly take uncertainty of the dynamics and/or of the system's environment into account, e.g., by including probabilistic chance constraints. However, SNMPC requires the approximate computation of the probability distributions for the state variables that are propagated through the nonlinear system dynamics. This invention proposes the use of Gaussian-assumed density filters (ADF) to perform high-accuracy propagation of mean and covariance information of the state variables through the nonlinear system dynamics, resulting in a tractable SNMPC approach with improved control performance. In addition, the use of a matrix factorization for the covariance matrix variables in the constrained optimal control problem (OCP) formulation guarantees positive definiteness of the full trajectory of covariance matrices in each iteration of any optimization algorithm. Finally, a tailored adjoint-based sequential quadratic programming (SQP) algorithm is described that considerably reduces the computational cost and allows a real-time feasible implementation of the proposed ADF-based SNMPC method to control nonlinear dynamical systems under uncertainty.