Optimality Conditions in Discrete Optimal Control Problems with State Constraints

Abstract

We consider nonlinear discrete optimal control problems with variable end points and with inequality and equality type constraints on trajectories and control. We derive first- and second-order necessary optimality conditions that are meaningful without a priori normality assumptions.

Keywords:

• Discrete optimal control
• Normality
• Optimality conditions

AMS Subject Classification:

• 90C46
• 49K

ACKNOWLEDGMENT

The author would like to thank A.V. Arutyunov for the valuable suggestions and the associate editor whose comments improved the presentation considerably.