A Method for Solving Optimal Control Problems Subject to Probabilistic Affine State Constraints for Linear Discrete-time Uncertain Systems

Recently, optimal control problems subject to probabilistic constraints have attracted much attention in many research fields. Although it is not straightforward to handle probabilistic constraints in an optimization problem, several methods haven been proposed to handle probabilistic constraints. This paper examines probabilistic constrained optimal control problems for linear discrete-time systems under uncertain disturbances with unknown probability distributions. The objective of this paper is to provide a method for solving the optimal control problems subject to probabilistic affine state constraints. Index Terms — Optimal Control, Stochastic Systems, Discrete-Time Systems, Probabilistic Constraints.