Chance-constrained state feedback control law design for nonlinear systems under uncertainties

A chance-constrained full-state feedback control law is designed to regulate nonlinear systems under uncertainties. The proposed scheme utilizes Monte Carlo sampling to generate multiple scenarios, formulates the optimal control problem as a scenario-based nonlinear optimization, and develops a sequential algorithm to obtain probabilistic feasible solutions. The resulting controller offers three advantages: First, the optimization-based design minimizes the tracking error across considered scenarios. Second, the sampling complexity is determined adaptively and the chance of constraint violation is bounded with a guaranteed confidence interval. Third, the sequential algorithm can reach a probabilistic feasible solution faster than directly using a state-of-the-art solver for the full-scenario optimization problem. Two case studies, including a CSTR and fermentor, are presented to demonstrate the effectiveness of the proposed method.