Stochastic Nonlinear Model Predictive Control with Joint Chance Constraints

When the stochastic description of system uncertainties is available, a natural approach to predictive control of uncertain systems involves explicitly accounting for the probabilistic occurrence of uncertainties in the optimal control problem. This work presents a stochastic nonlinear model predictive control (SNMPC) approach for nonlinear systems subject to time-invariant uncertainties as well as additive disturbances. The generalized polynomial chaos (gPC) framework is used to derive a deterministic surrogate for the stochastic optimal control problem. The key contribution of this paper lies in extending the gPC-based SNMPC approach reported in our earlier work to handle stochastic disturbances. This is done via mapping the stochastic disturbances onto the space of the coefficients of polynomial chaos expansions, which enables efficient propagation of stochastic disturbances. A sample-based approach to joint chance constraint handling is employed to fulfill the state constraints in a probabilistic sense. A gPC-based Bayesian parameter estimator is utilized to update the probability distribution of uncertain system parameters at each sampling time. In a simulation case study, the closed-loop performance of the SNMPC approach is demonstrated on an atmospheric-pressure plasma jet that is developed for biomedical applications.