Shooting methods to solve optimal control problems with state and mixed control-state constraints

Abstract

The paper presents two important approaches to solve numerically general optimal control problems with state and mixed control-state constraints. They may be attractive in the case, when the simple time discretization of the state equations and expressing the optimal control problem as a nonlinear mathematical programming problem is not sufficient. At the beginning an extension of the optimal control theory to problems with constraints on current state and on current state and control simultaneously is presented. Then, two approaches to solve numerically the emerging boundary value problems: indirect and direct shooting method are described and applied to an example problem.