Optimal trajectories associated to a solution of contingent Hamilton-Jacobi equation
Frankowska, Halina (1987), Optimal trajectories associated to a solution of contingent Hamilton-Jacobi equation, 26th IEEE Conference on Decision and Control, 1987. Proceedings, IEEE, p. 727-732. http://dx.doi.org/10.1109/CDC.1987.272464
Type
Communication / ConférenceDate
1987Conference title
26th IEEE Conference on Decision and Control, 1987Conference date
1987-12Conference city
Los AngelesConference country
États-UnisBook title
26th IEEE Conference on Decision and Control, 1987. ProceedingsPublisher
IEEE
Pages
727-732
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Metadata
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Frankowska, HalinaAbstract (EN)
In this paper we study the existence of optimal trajectories associated with a generalized solution to Hamilton-Jacobi-Bellman equation arising in optimal control. In general, we cannot expect such solutions to be differentiable. But, in a way analogous to the use of distributions in PDE, we replace the usual derivatives with "contingent epiderivatives" and the Hamilton-Jacobi equation by two "contingent Hamilton-Jacobi inequalities". We show that the value function of an optimal control problem verifies these "contingent inequalities". Our approach allows the following three results: (a) The upper semicontinuous solutions to contingent inequalities are monotone along the trajectories of the dynamical system. (b) With every continuous solution V of the contingent inequalities, we can associate an optimal trajectory along which V is constant. (c) For such solutions, we can construct optimal trajectories through the corresponding optimal feedback. They are also "viscosity solutions" of a Hamilton-Jacobi equation. Finally we discuss the link of viscosity solutions with Clarke's approach to the Hamilton-Jacobi equation.Subjects / Keywords
Differential equations; Viscosity; Optimal controlRelated items
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