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Optimal control of delay-differential inclusions with multivalued initial conditions in infinite dimensions

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EN
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EN
This paper is devoted to the study of a general class of optimal control problems described by delay-differential inclusions with infinite-dimensional state spaces, endpoints constraints, and multivalued initial conditions. To the best of our knowledge, problems of this type have not been considered in the literature, except for some particular cases when either the state space is finite-dimensional or there is no delay in the dynamics. We develop the method of discrete approximations to derive necessary optimality conditions in the extended Euler-Lagrange form by using advanced tools of variational analysis and generalized differentiation in infinite dimensions. This method consists of the three major parts: (a) constructing a well-posed sequence of discrete-time problems that approximate in an appropriate sense the original continuous-time problem of dynamic optimization; (b) deriving necessary optimality conditions for the approximating discrete-time problems by reducing them to infinite-dimensional problems of mathematical programming and employing then generalized differential calculus; (c) passing finally to the limit in the obtained results for discrete approximations to establish necessary conditions for the given optimal solutions to the original problem. This method is fully realized in the delay-differential systems under consideration.
Rocznik
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393--428
Opis fizyczny
Bibliogr. 15 poz.
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autor
Bibliografia
  • BORWEIN, J.M. and ZHU, Q.J. (2005) Techniques of Variational Analysis. CMS Books in Mathematics, 20, Springer, New York.
  • DIESTEL, J. and UHL, J.J. (1977) Vector Measures. American Mathematical Society, Providence, R.I.
  • DONTCHEV, A.L. and FARKHI, E.M. (1989) Error estimates for discretized differential inclusions. Computing, 41, 349-358.
  • MORDUKHOVICH, B.S. (1995) Discrete approximations and refined Euler-Lagrange conditions for nonconvex differential inclusions. SIAM Journal on Control and Optimization, 33, 882-815.
  • MORDUKHOVICH, B.S. (2006a) Variational Analysis and Generalized Differentiation, I: Basic Theory. Grundlehren Series (Fundamental Principles of Mathematics Sciences), 330, Springer, Berlin.
  • MORDUKHOVICH, B.S. (2006b) Variational Analysis and Generalized Differentiation, II: Applications. Grundlehren Series (Fundamental Principles of Mathematics Sciences), 331, Springer, Berlin.
  • MORDUKHOVICH, B.S. (2007) Variational analysis of evolution inclusions. SIAM Journal on Optimization, 18, 752-777.
  • MORDUKHOVICH, B.S. and WANG, D. (2005) Optimal control of semilinear evolution inclusions via discrete approximations. Control and Cybernetics, 34, 849-870.
  • MORDUKHOVICH, B.S. and WANG, L. (2003) Optimal control of constrained delay-differential inclusions with multivalued initial conditions, Control and Cybernetics, 28, 585-609.
  • MORDUKHOVICH, B.S. and WANG, L. (2004) Optimal control of neutral functional-differential inclusions, SIAM Journal on Control and Optimization, 43,111-136.
  • SCHIROTZEK, W. (2007) Nonsmooth Analysis. Series Universitext, Springer, Berlin.
  • SMIRNOV, G.V. (2002) Introduction to the Theory of Differential Inclusions. American Mathematical Society, Providence, R.I.
  • TOLSTONOGOV, A. A. (2000) Differential Inclusions in a Banach Space. Kluwer, Dordrecht, The Netherlands.
  • VINTER, R.B. (2000) Optimal Control. Birkhäuser, Boston.
  • WARGA, J. (1972) Optimal Control of Differential and Functional Equations. Academic Press, New York.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0031-0075
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