no. 2
Control problems governed by time-dependent maximal monotone operators
Saïdi, Soumia1 ; Yarou, Mustapha Fateh1
1 Laboratoire LMPA, Department of Mathematics, Jijel University, Algeria.
ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 2, pp. 455-473

The paper concerns on an infinite dimensional Hilbert space, the existence and uniqueness of absolutely continuous solutions, for Lipschitz single-valued perturbations of evolution problems involving maximal-monotone operators. This result allows us to extend to optimal control problems associated with such equations, the relaxation theorems with Young measures proved recently in [S. Saïdi, L. Thibault and M.F. Yarou, Numer. Funct. Anal. Optim. 34 (2013) 1156–1186].

Reçu le :
Accepté le :
DOI : 10.1051/cocv/2015056
Classification : 34A60, 49A52
Keywords: Maximal monotone operators, optimal control, pseudo-distance, Lipschitz perturbation, absolutely continuous, Young measures

Saïdi, Soumia 1 ; Yarou, Mustapha Fateh 1

1 Laboratoire LMPA, Department of Mathematics, Jijel University, Algeria. 
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Saïdi, Soumia; Yarou, Mustapha Fateh. Control problems governed by time-dependent maximal monotone operators. ESAIM: Control, Optimisation and Calculus of Variations, Tome 23 (2017) no. 2, pp. 455-473. doi: 10.1051/cocv/2015056

J.P. Aubin and A. Celina, Differential inclusions, Set-valued maps and viability theory. Springer-Verlag Berlin Heidelberg (1984). | Zbl | MR

H. Brézis, Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert. Lect. Notes Math. North-Holland (1973). | Zbl | MR

C. Castaing, A. Salvadori and L. Thibault, Functional evolution equations governed by nonconvex sweeping process. J. Nonlin. Convex Anal. 2 (2001) 217–241. | MR | Zbl

C. Castaing, A. Jofré and A. Salvadori, Control problems governed by functional evolution inclusions with Young measures. J. Nonlin. Convex Anal. 5 (2004) 131–152. | Zbl | MR

C. Castaing, P. Raynaud de Fitte and M. Valadier, Young measures on Topological Spaces With Applications in Control Theory and Probability Theory. Kluwer Academic Publishers, Dordrecht (2004). | Zbl | MR

J.F. Edmond and L. Thibault, Relaxation of an optimal control problem involving a perturbed sweeping process. Math. Program. Ser. B 104 (2005) 347–373. | Zbl | MR | DOI

A. Gouila-Houri, Sur la généralisation de la notion de commande d’un système guidable. Rev. Française Inform. Rech. Oper. 4 (1967) 7–32. | Zbl | Numdam | MR

A. Jawhar, Existence de solutions optimales pour des problèmes de contrôle de systèmes gouvernés par des équations différentielles multivoques. Sém. Anal. Convexe Montpellier exposé No, 1, Montpellier, France (1985). | Zbl | MR

V. Kunze and M.D.P. Monteiro Marques, BV solutions to evolution problems with time-dependent domains. Set-Valued Anal. 5 (1997) 57–72. | Zbl | MR | DOI

V. Lakshmikantham and S. Leela, Nonlinear Differential Equations in Abstract spaces. Pergamon Press, Oxford (1991). | Zbl | MR

M.D.P. Monteiro Marques, Differential Inclusions in Nonsmooth Mechanical Problems Shocks and Dry Friction. Birkhäuser-Verlag, Basel (1993). | Zbl | MR

J.J. Moreau, Evolution problem associated with a moving convex set in a Hilbert space. J. Differ. Eq. 26 (1977) 347–374. | Zbl | MR | DOI

S. Saïdi and M.F. Yarou, Control and viscosity results for problems governed by maximal monotone operators. To be submitted (2017).

S. Saïdi, L. Thibault and M.F. Yarou, Relaxation of optimal control problems involving time dependent subdifferential operators. Numer. Funct. Anal. Optim. 34 (2013) 1156–1186. | Zbl | MR | DOI

A.A. Vladimirov, Nonstationary dissipative evolution equations in a Hilbert space. Nonlin. Anal. 17 (1991) 499–518. | Zbl | MR | DOI

J. Warga, Optimal control of differential and functional equations. Academic Press, New York (1972). | Zbl | MR

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