Stochastic nonlinear model predictive control with probabilistic constraints

Stochastic uncertainties are ubiquitous in complex dynamical systems and can lead to undesired variability of system outputs and, therefore, a notable degradation of closed-loop performance. This paper investigates model predictive control of nonlinear dynamical systems subject to probabilistic parametric uncertainties. A nonlinear model predictive control framework is presented for control of the probability distribution of system states while ensuring the satisfaction of constraints with some desired probability levels. To obtain a computationally tractable formulation for real control applications, polynomial chaos expansions are utilized to propagate the probabilistic parametric uncertainties through the system model. The paper considers individual probabilistic constraints, which are converted explicitly into convex second-order cone constraints for a general class of probability distributions. An algorithm is presented for receding horizon implementation of the finite-horizon stochastic optimal control problem. The capability of the stochastic model predictive control approach in terms of shaping the probability distribution of system states and fulfilling state constraints in a stochastic setting is demonstrated for optimal control of polymorphic transformation in batch crystallization.