A Constraint-Tightening Approach to Nonlinear Model Predictive Control with Chance Constraints for Stochastic Systems

This paper presents a nonlinear model predictive control (NMPC) strategy for stochastic systems subject to chance constraints. The notion of stochastic tubes is extended to nonlinear systems to present a constraint tightening strategy that ensures stability and recursive feasibility of NMPC in the presence of stochastic uncertainties. State constraints are tightened recursively by constructing a sequence of sets from an initial constraint set, which is tightened using constraint backoff parameters obtained from either the probability distribution or the empirical cumulative distribution of the uncertainties. The performance of the NMPC strategy with chance constraints is compared to that of robust NMPC on a DC-DC converter benchmark case study.