Sufficient Optimality Conditions in Stability Analysis for State-Constrained Optimal Control

A family of parametric linear-quadratic optimal control problems is considered. The problems are subject to state constraints. It is shown that if weak second-order sufficient optimality conditions and standard constraint qualifications are satisfied at the reference point, then, for small perturbations of the parameter, there exists a locally unique stationary point, corresponding to a solution. This point is a Lipschitz continuous function of the parameter.