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Vector measures applied to optimal control for a class of evolution equations on Banach spaces

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In this paper we consider a class of nonlinear evolution equations on infinite dimensional Banach spaces driven by vector measures. We prove existence and uniqueness of solutions and continuous dependence of solutions on the control measures. Using these results we prove existence of optimal controls for Bolza problems. Based on this result we present necessary conditions of optimality.

Abstract

In this paper we consider a class of nonlinear evolution equations on infinite dimensional Banach spaces driven by vector measures. We prove existence and uniqueness of solutions and continuous dependence of solutions on the control measures. Using these results we prove existence of optimal controls for Bolza problems. Based on this result we present necessary conditions of optimality.

참고문헌 (11)

  1. N. U. Ahmed, "Semigroup theory with applications to systems and control" (1991), Longman Scientific & Technical
  2. N. U. Ahmed, "Some remarks on the dynamics of impulsive systems in Banach spaces", Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 8(2), pp.261~274 (2001)
  3. N. U. Ahmed, "Existence of optimal controls for a general class of impulsive systems on Banach spaces", SIAM J. Control Optim, 42(2), pp.669~685 (2003)[DOI]
  4. N. U. Ahmed, "Optimal relaxed controls for systems governed by impulsive differential inclusions", Nonlinear Funct. Anal. Appl, 10(3), pp.427~460 (2005)
  5. N. U. Ahmed, "Topological dual of B∞(I, L1(X, Y )) with application to stochastic systems on Hilbert space", Discuss. Math. Differ. Incl. Control Optim, 29, pp.67~90 (2009)[DOI]
  6. Ahmed N. U., "A CLASS OF NONLINEAR EVOLUTION EQUATIONS ON BANACH SPACES DRIVEN BY FINITELY ADDITIVE MEASURES AND ITS OPTIMAL CONTROL", Nonlinear Functional Analysis and Applications, 24(4), pp.837~864 (2019), 경남대학교 수학교육과[DOI]
  7. N. U. Ahmed, "Measure driven nonlinear dynamic systems with applications to optimal impulsive controls", ~
  8. J. Diestel, "Vector Measures" (1977), American Mathematical Society
  9. N. Dunford, "Linear Operators. Part I" (1988), Wiley Classics Library, John Wiley & Sons, Inc.
  10. A. C. Gavrilut¸, "A Gould type integral with respect to a submeasure", An. S¸tiint¸. Univ. Al. I. Cuza Ia¸si. Mat. (N.S.), 53(2), pp.351~368 (2007)
  11. G. G. Gould, "Integration over vector-valued measures", Proc. London Math. Soc. (3), 15, pp.193~225 (1965)[DOI]

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