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Volumn 35, Issue 4, 1997, Pages 1297-1327

Pontryagin's principle for state-constrained boundary control problems of semilinear parabolic equations

Author keywords

Boundary control; Optimality conditions; Pontryagin principle; Semilinear parabolic equations; State constraints

Indexed keywords

CONSTRAINT THEORY; CONTROL THEORY; OPTIMIZATION; PERTURBATION TECHNIQUES; THEOREM PROVING;

EID: 0031189751     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012995283637     Document Type: Article
Times cited : (242)

References (33)
  • 2
    • 0001168467 scopus 로고
    • On the local behaviour of solutions of degenerate parabolic equations with measurable coefficients
    • E. DI BENEDETTO, On the local behaviour of solutions of degenerate parabolic equations with measurable coefficients, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 13 (1986), pp. 487-535.
    • (1986) Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) , vol.13 , pp. 487-535
    • Di Benedetto, E.1
  • 3
    • 0000930026 scopus 로고
    • Non-linear elliptic and parabolic equations involving measure data
    • L. BOCCARDO AND T. GALLOUËT, Non-linear elliptic and parabolic equations involving measure data, J. Funct. Anal., 87 (1989), pp. 149-169.
    • (1989) J. Funct. Anal. , vol.87 , pp. 149-169
    • Boccardo, L.1    Gallouët, T.2
  • 4
    • 0026382279 scopus 로고
    • Pontryagin's principle for the optimal control of semilinear elliptic systems with state constraints
    • Brighton, England
    • J. BONNANS, Pontryagin's principle for the optimal control of semilinear elliptic systems with state constraints, in 30th IEEE Conference on Control and Decision, Brighton, England, 1991, pp. 1976-1979.
    • (1991) 30th IEEE Conference on Control and Decision , pp. 1976-1979
    • Bonnans, J.1
  • 5
    • 0346959189 scopus 로고
    • Un principe de Pontryagine pour le contrôle des systèmes elliptiques
    • J. BONNANS AND E. CASAS, Un principe de Pontryagine pour le contrôle des systèmes elliptiques, J. Differential Equations, 90 (1991), pp. 288-303.
    • (1991) J. Differential Equations , vol.90 , pp. 288-303
    • Bonnans, J.1    Casas, E.2
  • 6
    • 0001654425 scopus 로고
    • An extension of Pontryagin's principle for state-constrained optimal control of semilinear elliptic equations and variational inequalities
    • J. BONNANS AND E. CASAS, An extension of Pontryagin's principle for state-constrained optimal control of semilinear elliptic equations and variational inequalities, SIAM J. Control Optim., 33 (1995), pp. 274-298.
    • (1995) SIAM J. Control Optim. , vol.33 , pp. 274-298
    • Bonnans, J.1    Casas, E.2
  • 7
    • 0022810709 scopus 로고
    • Control of an elliptic problem with pointwise state constraints
    • E. CASAS, Control of an elliptic problem with pointwise state constraints, SIAM J. Control Optim., 24 (1986), pp. 1309-1318.
    • (1986) SIAM J. Control Optim. , vol.24 , pp. 1309-1318
    • Casas, E.1
  • 8
    • 3943065938 scopus 로고
    • Finite element approximations for some state-constrained optimal control problems
    • P. Borne, S. Tzafestas, and N. Radhy, eds., North Holland, Amsterdam
    • E. CASAS, Finite element approximations for some state-constrained optimal control problems, in Mathematics of the Analysis and Design in Process Control, P. Borne, S. Tzafestas, and N. Radhy, eds., North Holland, Amsterdam, 1992, pp. 293-301.
    • (1992) Mathematics of the Analysis and Design in Process Control , pp. 293-301
    • Casas, E.1
  • 10
    • 0027623859 scopus 로고
    • Boundary control of semilinear elliptic equations with pointwise state constraints
    • E. CASAS, Boundary control of semilinear elliptic equations with pointwise state constraints, SIAM J. Control Optim., 31 (1993), pp. 993-1006.
    • (1993) SIAM J. Control Optim. , vol.31 , pp. 993-1006
    • Casas, E.1
  • 11
    • 3943080899 scopus 로고
    • Pontryagin's principle for optimal control problems governed by semilinear elliptic equations
    • F. Kappel and K. Kunisch, eds., Birkhäuser, Basel
    • E. CASAS, Pontryagin's principle for optimal control problems governed by semilinear elliptic equations, in International Conference on Control and Estimation of Distributed Parameter Systems: Nonlinear Phenomena, F. Kappel and K. Kunisch, eds., Birkhäuser, Basel, 1994, pp. 97-114.
    • (1994) International Conference on Control and Estimation of Distributed Parameter Systems: Nonlinear Phenomena , pp. 97-114
    • Casas, E.1
  • 12
    • 0030150290 scopus 로고    scopus 로고
    • Boundary control problems of quasilinear elliptic equations: A Pontryagin's principle
    • E. CASAS, Boundary control problems of quasilinear elliptic equations: A Pontryagin's principle, Appl. Math. Optim., 33 (1996), pp. 265-291.
    • (1996) Appl. Math. Optim. , vol.33 , pp. 265-291
    • Casas, E.1
  • 13
    • 3943100197 scopus 로고
    • A Green's formula for quasilinear parabolic operators
    • C. Perelló, C. Simó, and J. Solá-Morales, eds., World Scientific Publishing, Singapore
    • E. CASAS AND L. FERNÁNDEZ, A Green's formula for quasilinear parabolic operators, in Equadiff 91. International Conference on Differential Equations, C. Perelló, C. Simó, and J. Solá-Morales, eds., World Scientific Publishing, Singapore, 1993, pp. 363-367.
    • (1993) Equadiff 91. International Conference on Differential Equations , pp. 363-367
    • Casas, E.1    Fernández, L.2
  • 14
    • 84972525877 scopus 로고
    • Maximum principle for state-constrained optimal control problems governed by quasilinear elliptic equations
    • E. CASAS AND J. YONG, Maximum principle for state-constrained optimal control problems governed by quasilinear elliptic equations, Differential Integral Equations, 8 (1995), pp. 1-18.
    • (1995) Differential Integral Equations , vol.8 , pp. 1-18
    • Casas, E.1    Yong, J.2
  • 16
    • 84966198944 scopus 로고
    • Nonconvex minimization problems
    • I. EKELAND, Nonconvex minimization problems, Bull. Amer. Math. Soc., 1 (1979), pp. 76-91.
    • (1979) Bull. Amer. Math. Soc. , vol.1 , pp. 76-91
    • Ekeland, I.1
  • 17
    • 0010018021 scopus 로고
    • ∞ spaces
    • Optimal Control of Partial Differential Equations, K. Hoffmann and W. Krabs, eds., Springer-Verlag, Berlin
    • ∞ spaces, in Optimal Control of Partial Differential Equations, Lecture Notes in Control and Information Sciences 149, K. Hoffmann and W. Krabs, eds., Springer-Verlag, Berlin, 1991, pp. 60-80.
    • (1991) Lecture Notes in Control and Information Sciences , vol.149 , pp. 60-80
    • Fattorini, H.1
  • 18
    • 0027694146 scopus 로고
    • Optimal control problems for distributed parameter systems in Banach spaces
    • H. FATTORINI, Optimal control problems for distributed parameter systems in Banach spaces, Appl. Math. Optim., 4 (1993), pp. 225-257.
    • (1993) Appl. Math. Optim. , vol.4 , pp. 225-257
    • Fattorini, H.1
  • 19
    • 0025867927 scopus 로고
    • Infinite dimensional control problems with state constraints
    • Proceedings of IFIP-IIASA Conference on Modelling and Inverse Problems of Control for Distributed Parameter Systems, Springer-Verlag, Berlin
    • H. FATTORINI AND H. FRANKOWSKA, Infinite dimensional control problems with state constraints, in Proceedings of IFIP-IIASA Conference on Modelling and Inverse Problems of Control for Distributed Parameter Systems, Lecture Notes in Control and Information Sciences 154, Springer-Verlag, Berlin, 1991, pp. 52-62.
    • (1991) Lecture Notes in Control and Information Sciences , vol.154 , pp. 52-62
    • Fattorini, H.1    Frankowska, H.2
  • 20
    • 84972519728 scopus 로고
    • Optimal controls problems for nonlinear parabolic boundary control systems: The Dirichlet boundary condition
    • H. FATTORINI AND T. MURPHY, Optimal controls problems for nonlinear parabolic boundary control systems: the Dirichlet boundary condition, Differential Integral Equations, 6 (1994), pp. 1367-1388.
    • (1994) Differential Integral Equations , vol.6 , pp. 1367-1388
    • Fattorini, H.1    Murphy, T.2
  • 21
    • 0028538715 scopus 로고
    • Optimal controls problems for nonlinear parabolic boundary control systems
    • H. FATTORINI AND T. MURPHY, Optimal controls problems for nonlinear parabolic boundary control systems, SIAM J. Control Optim., 32 (1994), pp. 1577-1596.
    • (1994) SIAM J. Control Optim. , vol.32 , pp. 1577-1596
    • Fattorini, H.1    Murphy, T.2
  • 24
    • 0019171913 scopus 로고
    • State constrained control problems for parabolic systems: Regularity of optimal solutions
    • I. LASIECKA, State constrained control problems for parabolic systems: Regularity of optimal solutions, Appl. Math. Optim., 6 (1980), pp. 1-29.
    • (1980) Appl. Math. Optim. , vol.6 , pp. 1-29
    • Lasiecka, I.1
  • 25
    • 0020500320 scopus 로고
    • Vector-valued measure and the necessary conditions for the optimal control problems of linear systems
    • Toulouse, France
    • X. LI, Vector-valued measure and the necessary conditions for the optimal control problems of linear systems, in Proc. IFAC 3rd Symposium on Control of Distributed Parameter Systems, Toulouse, France, 1982.
    • (1982) Proc. IFAC 3rd Symposium on Control of Distributed Parameter Systems
    • Li, X.1
  • 26
    • 0039177194 scopus 로고
    • Maximum principle of distributed parameter systems with time lags
    • Distributed Parameter Systems, Springer-Verlag, New York
    • X. LI AND Y. YAO, Maximum principle of distributed parameter systems with time lags, in Distributed Parameter Systems, Lecture Notes in Control and Information Sciences 75, Springer-Verlag, New York, 1985, pp. 410-427.
    • (1985) Lecture Notes in Control and Information Sciences , vol.75 , pp. 410-427
    • Li, X.1    Yao, Y.2
  • 27
    • 0026188882 scopus 로고
    • Necessary conditions of optimal control for distributed parameter systems
    • X. LI AND J. YONG, Necessary conditions of optimal control for distributed parameter systems, SIAM J. Control Optim., 29 (1991), pp. 895-908.
    • (1991) SIAM J. Control Optim. , vol.29 , pp. 895-908
    • Li, X.1    Yong, J.2
  • 28
    • 0348172679 scopus 로고
    • Problèmes aux limites non homogènes IV
    • J. LIONS, Problèmes aux limites non homogènes IV, Ann. Scuola Norm. Sup. Pisa, 15 (1961), pp. 311-236.
    • (1961) Ann. Scuola Norm. Sup. Pisa , vol.15 , pp. 311-1236
    • Lions, J.1
  • 30
    • 0000281633 scopus 로고
    • Pathological solutions of elliptic differential equations
    • J. SERRIN, Pathological solutions of elliptic differential equations, Ann. Scuola Norm. Sup. Pisa, 18 (1964), pp. 385-387.
    • (1964) Ann. Scuola Norm. Sup. Pisa , vol.18 , pp. 385-387
    • Serrin, J.1
  • 32
    • 0012069008 scopus 로고
    • On some parabolic boundary control problems with constraints on the control and functional-constraints on the state
    • F. TRÖLTZSCH, On some parabolic boundary control problems with constraints on the control and functional-constraints on the state, Z. Anal. Anwendungen, 1 (1982), pp. 1-13.
    • (1982) Z. Anal. Anwendungen , vol.1 , pp. 1-13
    • Tröltzsch, F.1
  • 33
    • 84972537249 scopus 로고
    • Pontryagin maximum principle for semilinear second order elliptic partial differential equations and variational inequalities with state constraints
    • J. YONG, Pontryagin maximum principle for semilinear second order elliptic partial differential equations and variational inequalities with state constraints, Differential Integral Equations, 5 (1992), pp. 1307-1334.
    • (1992) Differential Integral Equations , vol.5 , pp. 1307-1334
    • Yong, J.1


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