zbMATH — the first resource for mathematics

Optimization and identification of nonlinear uncertain systems. (English) Zbl 1080.49500
Summary: In this paper we consider the optimal control of both operators and parameters for uncertain systems. For the optimal control and identification problem, we show the existence of an optimal solution and present necessary conditions for optimality.

49J20 Existence theories for optimal control problems involving partial differential equations
49K20 Optimality conditions for problems involving partial differential equations
49K24 Optimal control problems with differential inclusions (nec./ suff.) (MSC2000)
Full Text: DOI EuDML
[1] N. U. Ahmed: Optimization and Identification of Systems Governed by Evolution Equations on Banach Space. Pitman Res. Notes Math. Ser. 184. Longman, Harlow, 1988.
[2] N. U. Ahmed: Optimal control of infinite-dimensional systems governed by functional differential inclusions. Disc. Math. Diff. Inclusions 15 (1995), 75-94. · Zbl 0824.49007
[3] N. U. Ahmed and K. L. Teo: Optimal Control of Distributed Parameter Systems. North-Holland, Amsterdam, 1981. · Zbl 0472.49001
[4] N. U. Ahmed and X. Xing: Nonlinear uncertain systems and necessary conditions of optimality. SIAM J. Control Optim. 35 (1997), 1755-1772. · Zbl 0907.49014 · doi:10.1137/S0363012995285569
[5] V. Barbu: Analysis and Control of Nonlinear Infinite Dimensional Systems. Academic press, INC, Boston-Sandiego-New York-London-Sydney-Tokyo-Toronto, 1993. · Zbl 0776.49005
[6] R. Dautray and J. L. Lions: Mathematical Analysis and Numerical Methods for Science and Technology, Vol. 5. Springer-Verlag, Berlin-Heidelberg, 1992.
[7] N. U. Papageorgionu: Nonlinear Volterra integrodifferential evolution inclusions and optimal control. Kodai Math. J. 14 (1991), 254-280. · Zbl 0768.49005 · doi:10.2996/kmj/1138039398
[8] N. U. Papageorgionu: Identification of parameters in systems governed by nonlinear evolution equations. Publ. Math. Debrecen 46 (1995), 215-237.
[9] N. U. Papageorgionu: On the optimal control of strongly nonlinear evolution equations. J. Math. Anal. Appl. 164 (1992), 83-103. · Zbl 0766.49010 · doi:10.1016/0022-247X(92)90146-5
[10] J. Y. Park, J. H. Ha and H. K. Han: Identification problem for damping parameters in linear damped second order systems. J. Korean Math. Soc. 34 (1997), 895-909. · Zbl 0894.35062
[11] J. Y. Park, Y. H. Kang and I. H. Jung: Optimization and identification of nonlinear systems on Banach space. Indian J. Pure Appl. 32 (2001), 633-647. · Zbl 0978.49006
[12] J. Y. Park, Y. H. Kang and M. J. Lee: Optimal control problem for the nonlinear hyperbolic systems. RIMS Kokyuroku 1187 (2001), 27-36. · Zbl 0985.49502
[13] E. Zeidler: Nonlinear functional analysis and its applications, II. Springer-Verlag, New York, 1990. · Zbl 0684.47029
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.