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Sensitivity and Controllability of Systems Governed by Integral Equations Via Proximal Analysis

Published online by Cambridge University Press:  20 November 2018

A. Yezza
A. Yezza*
Affiliation:
Departement de mathematiques et de statistique Universite de Montreal C.P. 6128-A Montreal, Quebec H3C 3J7
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Abstract

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In this paper, we are concerned with the basic problem defined in [9]. Formulas for δV(0)and δ∞V(0),respectively the generalized and asymptotic gradient of the value function at zero, corresponding to an L2 -additive perturbation of dynamics are given. Under the normality condition, δV(0)turns out to be a compact subset of L2, formed entirely of arcs, and V is locally finite and Lipschitz at 0. Moreover, estimations of the generalized directional derivative and Dini's derivative of V at 0 are derived. Supplementary conditions imply that Dini's derivative of V at 0 exists, and V is actually strictly differentiate at this point.

Keywords

49E2593B0593B3593C22Optimal controlvalue functionsensitivitycontrollabilityproximal normal analysisgeneralized gradientgeneralized asymptotic gradientVolterra integral equation
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 45 , Issue 5 , 01 October 1993 , pp. 1104 - 1120
Copyright
Copyright © Canadian Mathematical Society 1993

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