Lipschitzianity of optimal trajectories for the Bolza optimal control problem

Frankowska, H.; Marchini, E. M.
December 2006
Calculus of Variations & Partial Differential Equations;Dec2006, Vol. 27 Issue 4, p467
Academic Journal
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.


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