Lipschitzianity of optimal trajectories for the Bolza optimal control problem |
| |
Authors: | H. Frankowska E. M. Marchini |
| |
Affiliation: | (1) CREA, école Polytechnique, 1 Rue Descartes, 75005 Paris, France |
| |
Abstract: | In this paper we investigate Lipschitz continuity of optimal solutions for the Bolza optimal control problem under Tonelli’s type growth condition. Such regularity being a consequence of normal necessary conditions for optimality, we propose new sufficient conditions for normality of state-constrained nonsmooth maximum principles for absolutely continuous optimal trajectories. Furthermore we show that for unconstrained problems any minimizing sequence of controls can be slightly modified to get a new minimizing sequence with nice boundedness properties. Finally, we provide a sufficient condition for Lipschitzianity of optimal trajectories for Bolza optimal control problems with end point constraints and extend a result from (J. Math. Anal. Appl. 143, 301–316, 1989) on Lipschitzianity of minimizers for a classical problem of the calculus of variations with discontinuous Lagrangian to the nonautonomous case. |
| |
Keywords: | Optimal control Calculus of variations Bolza problem Lipschitzian regularity Normality of the maximum principle |
本文献已被 SpringerLink 等数据库收录! |