Some Characterizations of Optimal Trajectories in Control Theory

Cannarsa, P. & Frankowska, H. (1989). Some Characterizations of Optimal Trajectories in Control Theory. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-89-083

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Abstract

The authors provide several characterizations of optimal trajectories for the classical Meyer problem arising in optimal control. For this purpose they study the regularity of directional derivatives of the value function: for instance it is shown that for smooth control systems the value function V is continuously differentiable along an optimal trajectory x. Then they deduce the upper semicontinuity of the optimal feedback map and address the problem of optimal design, obtaining sufficient conditions for optimality. Finally it is shown that the optimal control problem may be reduced to a viability problem.

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