Geodesic
Sensitivity and Controllability of Systems Governed by Integral Equations Via Proximal Analysis
Canadian journal of mathematics, Tome 45 (1993) no. 5, pp. 1104-1120

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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 L 2 -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.
DOI : 10.4153/CJM-1993-061-0
Mots-clés : 49E25, 93B05, 93B35, 93C22, Optimal control, value function, sensitivity, controllability, proximal normal analysis, generalized gradient, generalized asymptotic gradient, Volterra integral equation 
Yezza, A. Sensitivity and Controllability of Systems Governed by Integral Equations Via Proximal Analysis. Canadian journal of mathematics, Tome 45 (1993) no. 5, pp. 1104-1120. doi: 10.4153/CJM-1993-061-0
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[1] 1. Borwein, J.M. and Giles, J.R., The proximal normal formula in Banach space, Trans. Amer. Math. Soc. 302(1987), 371–381. Google Scholar

[2] 2. Borwein, J.M. and Strojwas, H.M., Proximal analysis and boundaries of closed sets in Banach space, Part I: Theory, Can. J. Math. (2) XXXVIII(1986), 431–452. Google Scholar

[3] 3. Borwein, J.M. and Strojwas, H.M., Proximal analysis and boundaries of closed sets in Banach space, Part II: Applications, Can. J. Math. (2) XXXIX(1987), 428–472. Google Scholar

[4] 4. Clarke, F.H., Optimization and Nonsmooth Analysis, Wiley-Interscience, New York, 1983. second edition 1990, Classics in Applied Math., SIAM, Philadelphia. Google Scholar

[5] 5. Clarke, F.H., Perturbed optimal control problems, IEEE Transactions on Automatic Control (6) AC31(1986), 535–542. Google Scholar

[6] 6. Loewen, P.D., The proximal normal formula in Hubert space, Nonlinear Analysis, Theory and Applications (9) 11(1987), 979–995. Google Scholar

[7] 7. Raissi, N., Analyse Proximate en Optimisation, Ph.D. thesis, Université de Montréal, 1987. Google Scholar

[8] 8. Yezza, A., Optimisation des Systèmes Gouvernés par des Equations Intégrales, Ph.D. thesis, Université de Montréal, 1991. Google Scholar

[9] 9. Yezza, A., Relaxed optimal control problems governed by integral equations,]. Math. Anal and Appl., (1993), to appear. Google Scholar

[10] 10. Warga, J., Optimal Control of Differential and Functional Equations, Academic Press, New York/London, 1972. Google Scholar

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