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2007 | 27 | 1 | 135-150
Tytuł artykułu

Sufficient optimality conditions for multivariable control problems

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EN
Abstrakty
EN
We study optimal control problems for partial differential equations (focusing on the multidimensional differential equation) with control functions in the Dirichlet boundary conditions under pointwise control (and we admit state - by assuming weak hypotheses) constraints.
Twórcy
  • Faculty of Mathematics, University of Łódź, Banacha 22, 90-238 Łódź, Poland
Bibliografia
  • [1] N. Arada and J.P. Raymond, Optimality conditions for state-constrained Dirichlet boundary control problems, J. Optim. Theory Appl. 102 (1999), 51-68.
  • [2] N. Arada and J.P. Raymond, Dirichlet boundary control of semilinear parabolic equations, Part 2: Problems with pointwise state constraints, Appl. Math. Optim. 45 (2002), 145-167.
  • [3] V. Barbu, Analysis and control of nonlinear infinite dimensional systems, Academic Press, Boston 1993.
  • [4] V. Barbu, The dynamic programming equation for the time-optimal control problem in infinite dimensions, SIAM J. Control Optim. 29 (1991), 445-456.
  • [5] V. Barbu and G. Da Prato, Hamilton-Jacobi equations in Hilbert spaces, Pitman Advanced Publishing Program, Boston 1983.
  • [6] P. Cannarsa and O. Carja, On the Bellman equation for the minimum time problem in infinite dimensions, SIAM J. Control Optim. 43 (2004), 532-548.
  • [7] E. Casas, Pontryagin's principle for state-constrained boundary control problems of semilinear parabolic equations, SIAM J. Control Optim. 35 (1997), 1297-1327.
  • [8] H.O. Fattorini, Infinite-Dimensional Optimization and Control Theory, Cambridge University Press, Cambridge, 1999.
  • [9] H.O. Fattorini and T. Murphy, Optimal control for nonlinear parabolic boundary control systems: the Dirichlet boundary conditions, Diff. Integ. Equ. 7 (1994), 1367-1388.
  • [10] A.V. Fursikov, Optimal control of distributed systems. Theory and applications, American Mathematical Society, Providence, RI 2000.
  • [11] F. Gozzi and M.E. Tessitore, Optimality conditions for Dirichlet boundary control problems of parabolic type, J. Math. Systems Estim. Control (1998), 8.
  • [12] E. Galewska and A. Nowakowski, Multidimensional Dual Dynamic Programming, Journal of Optimization Theory and Applications 124 (2005), 175-186.
  • [13] E. Galewska and A. Nowakowski, A dual dynamic programming for multidimensional elliptic optimal control problems, Numerical Functional Analysis and Optimization-accepted in July 2005.
  • [14] I. Lasiecka, J.L. Lions and R. Triggiani, Nonhomogeneous boundary value problems for second order hyperbolic operators, J. Math. Pures Appl. 65 (1986), 149-192.
  • [15] X. Li and J. Yong, Optimal control theory for infinite dimensional systems, Birkhauser, Boston 1994.
  • [16] B.S. Mordukhovich and K. Zhang, Minimax control of parabolic systems with Dirichlet boundary conditions and state constraints, Appl. Math. Optim. 36 (1997), 323-360.
  • [17] B.S. Mordukhovich and K. Zhang, Dirichlet boundary control of parabolic systems with pointwise state constraints in International Conference on Control and Estimations of Distributed Parameter Systems, in Control and Estimation of Distributed Parameter Systems (Vorau, 1996), Intentational Series of Numerrical Mathematics, Vol. 126, Birkhäuser. Basel (1998), 223-236.
  • [18] B.S. Mordukhovich and J.P. Raymond, Dirichlet boundary control of hyperbolic equations in the presence of state constraints, Appl. Math. Optim. 49 (2004), 145-157
  • [19] B.S. Mordukhovich and J.P. Raymond, Neumann boundary control of hyperbolic equations with pointwise state constraints, SIAM J. Control Optim. 43 (2004), 1354-1372.
  • [20] P. Neittaanmaki and D. Tiba, Optimal control of nonlinear parabolic systems, Marcel Dekker, New York 1994.
  • [21] A. Nowakowski, The dual dynamic programming, Proc. Amer. Math. Soc. 116 (1992), 1089-1096.
  • [22] J.P. Raymond, Nonlinear boundary control of semilinear parabolic problems with pointwise state constraints, Discrete Contin. Dynam. Systems 3 (1997), 341-370.
  • [23] L.W. White, Control of a hyperbolic problem with pointwise stress constraints, J. Optim. Theory Appl. 41 (1983), 359-369.
  • [24] L.W. White, Distributed control of a hyperbolic problem with control and stress constraints, J. Math. Anal. Appl. 106 (1985), 41-53.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1080
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