Uncertainty Propagation by Linear Regression Kalman Filters for Stochastic NMPC


Stochastic nonlinear model predictive control (SNMPC) allows to directly take model uncertainty into account, e.g., by including probabilistic chance constraints. This paper proposes linear-regression Kalman filtering to perform high-accuracy propagation of mean and covariance information for the nonlinear system dynamics in a tractable approximation of the stochastic optimal control problem. In addition, a tailored adjoint-based sequential quadratic programming (SQP) algorithm is presented to considerably reduce the computational cost and allow a real-time implementation of the resulting SNMPC. The prediction accuracy and control performance of the proposed approach are illustrated on a vehicle control application subject to external disturbances, while highlighting a worst-case computation time of 10 ms for SNMPC which is close to that of deterministic NMPC for this particular case study.