BOULIGAND DIFFERENTIABILITY OF SOLUTIONS TO PARAMETRIC OPTIMAL CONTROL PROBLEMS^*

Abstract

A family of parameter dependent optimal control problems for nonlinear ODEs is considered. The problems are subject to pointwise control constraints. It is shown that the standard conditions, used in stability analysis of optimal control problems, ensure not only Lipschitz continuity, but also Bouligand differentiability of the solutions with respect to the parameter. The Bouligand differentials are characterized as the solutions to the accessory linear-quadratic optimal control problems.

^*Supported by the Polish State Committee for Scientific Research (KBN) grant 8 T11A 028 14.

Keywords:

• Parametric optimal control
• Nonlinear ordinary differential equations
• Control constraints
• Bouligand differentiability of the solutions

Acknowledgments

Notes

^*Supported by the Polish State Committee for Scientific Research (KBN) grant 8 T11A 028 14.