SOME GEOMETRIC ASPECTS OF OPTIMAL CONTROL PROBLEMS WITH STATE INEQUALITY CONSTRAINTS.
CALIFORNIA UNIV BERKELEY INST OF ENGINEERING RESEARCH
Pagination or Media Count:
This thesis deals with the investigation of geometric aspects of optimal control problems with state inequality constraints. An unrestricted maximum principle is derived, whose associated adjoint equation possesses a solution which is continuous, except under special circumstances, even at junction points of an optimal trajectory with the state boundary. This result is shown to be valid under the assumption of regularity in the sense of Pontryagin as well as for certain non-regular problems. The relation between the unrestricted maximum principle and the restricted one of Pontryagin is demonstrated. This investigation is based on the geometric notions introduced by Blaquiere and Leitmann and constitutes an extension of their work to problems with state variable inequality constraints. This geometric approach is contrasted with the approach of Dynamic Programming. Author