Linear Optimal Control Problems and Generalized Linear Programs

Linear optimal control problems with state inequality constraints is an important class of large systems. This paper shows that a generalized programming formulation of these problems does not result in a decomposition over time or a maximum principle as it does for problems without the state constraints. A semi-infinite generalized programming formulation, however, can be used to formally produce the maximum principle, i.e. the necessary optimality conditions, for problems under consideration