Analogue of the Kelley condition for optimal systems with retarded control

ABSTRACT

In this paper, we consider an optimal control problem with retarded control and study a larger class of singular (in the classical sense) controls. The Kelley and equality type optimality conditions are obtained. To prove our main results, we use the Legendre polynomials as variations of control.

KEYWORDS:

• Singular control
• optimal control
• variation transform method
• Legendre polynomial
• Kelley type optimality condition
• equality type optimality condition

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.