On the constrained optimal control problems with mixed constraints

Résumé

The analytical solutions of optimal control problems with mixed constraints are examined. The analytical solutions are obtained by applying the first order optimality conditions on the Lagrangian function. The method of fundamental matrix is then used to solve the resulting non-homogeneous system of first order ordinary differential equations. This leads to the analytical solutions of the state and control variables and the objective function value. Two examples of optimal control problems constrained by ordinary differential equations and inequalities are considered.