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2012 | 32 | 1 | 87-109
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Stochastic diffrential equations on Banach spaces and their optimal feedback control

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In this paper we consider stochastic differential equations on Banach spaces (not Hilbert). The system is semilinear and the principal operator generating a C₀-semigroup is perturbed by a class of bounded linear operators considered as feedback operators from an admissible set. We consider the corresponding family of measure valued functions and present sufficient conditions for weak compactness. Then we consider applications of this result to several interesting optimal feedback control problems. We present results on existence of optimal feedback operators.
  • [1] N.U. Ahmed, Semigroup Theory with Applications to Systems and Control, Pitman Research Notes in Mathematics series 246 (1999) Longman Scientific and Technical, U.K.
  • [2] N.U. Ahmed, Generalized solutions of HJB equations applied to stochastic control on Hilbert space, Nonlinear Analysis 54 (2003) 495-523. doi: 10.1016/S0362-546X(03)00109-3
  • [3] N.U. Ahmed, Optimal relaxed controls for infinite dimensional stochastic systems of Zakai type, SIAM J. Control and Optimization 34 (5) (1996) 1592-1615. doi: 10.1137/S0363012994269119
  • [4] N.U. Ahmed, Optimal control of ∞-dimensional stochastic systems via generalized solutions of HJB equations, Discuss. Math. Differential Inclusions, Control and Optimization 21 (2001) 97-126.
  • [5] N.U. Ahmed and K.L. Teo, Optimal Control of Distributed Parameter Systems, North Holland, New York, Oxford, 1981.
  • [6] L. Cesari, Optimization Theory and Applications, Springer-Verlag, 1983.
  • [7] G. Da Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions, Cambridge University Press, 1992.
  • [8] N. Dnford and J.T. Schwartz, Linear Operators, Part 1, Inter Science Publishers, Inc., New York, 1958.
  • [9] J. Diestel and J.J. Uhl Jr., Vector Measures, in: Mathematical surveys, Vol. 15, American Mathematical Society, Providence, RI, 1977.
  • [10] H.O. Fattorini, Infinite Dimensional optimization and Control Theory, Encyclopedia of mathematics and its applications, 62, Cambridge University Press, 1999.
  • [11] F. Gozzi, E. Rouy and A. Swiech, Second order Hamilton-Jacobi equation in Hilbert spaces and stochastic boundary control, SIAM J. Control Optim. 38 (2000) 400-430. doi: 10.1137/S0363012997324909
  • [12] B. Goldys and B. Maslowski, Ergodic Control of Semilinear Stochastic Equations and Hamilton-Jacobi Equations, preprint, 1998.
  • [13] P. Mattila and D. Mauldin, Measure and dimension functions: measurability and densities, Math. Proc. Camb. Phil. Soc. 121 (1997) 81-100. doi: 10.1017/S0305004196001089
  • [14] K.R. Parthasarathy, Probability Measures on Metric Spaces, Academic Press, New York and London, 1967.
  • [15] A.I. Tulcea and C.I. Tulcea, Topics in the Theory of Lifting, Springer-Verlag, Berlin, Heidelberg, New York, 1969.
  • [16] A. Weron, On Weak second order and Gaussian random elements, Lecture Notes in Mathematics 526 (1976) 263-272, DOI: 10.1007/BFb0082336, Proceedings of the First International Conference on Probability in Banach Spaces, 20-26 July 1975, Oberwolfach. doi: 10.1007/BFb0082336
  • [17] J. Motyl, Existence of solutions of functional stochastic inclusions, Dynamic Systems and Applications (DSA) 21 (2012) 331-338.
  • [18] M. Kozaryn, M.T. Malinowski, M. Michta and K.L. Ŝwiatek, On multivalued stochastic integral equations driven by a Wiener process in the plane, Dynamic Systems and Applications (DSA) 21 (2012) 293-318.
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