On necessary optimality conditions in discrete control systems

Abstract

The paper deals with a nonlinear discrete-time optimal control problem with a cost functional of terminal type. Using a new variation of the control and new properties of optimal controls, we prove the linearised optimality conditions extending such classical optimality conditions. Along with this, various optimality conditions of quasi-singular controls are obtained. Finally, the examples illustrating the rich content of the obtained results are illustrated.

Keywords:

• discrete system
• optimality conditions
• maximum principle
• optimal control

Acknowledgements

The authors would like to thank all referees for their helpful comments that have improved the presentation of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.