Maximum principle for Volterra integral equations with controlled delay time

Abstract

Optimal control problems are considered for a special class of nonlinear Volterra integral equations with unknown functions in the limits of integration. The equations describe the renewal of age-dependent capital equipment under technological change. A dual system and a maximum principle are established for such problems.

Keywords:

• Optimal control
• Volterra integral equations
• Controlled delay
• Maximum principle
• Mathematics Subjects Classifications 2000: 49J22
• 49K22

Acknowledgements

The author is grateful to the anonymous referees for the valuable remarks that essentially improved the article. He wishes to thank the Editor-In-Chief for timely feedback.