×

Optimal feedback control for a class of strongly nonlinear impulsive evolution equations. (English) Zbl 1122.49030

Summary: We consider the optimal feedback control problems of a system governed by strongly nonlinear impulsive differential equations which contains monotone operators and nonlinear nonmonotone perturbations. Based on the existence of feasible pairs, an existence result of optimal control pairs for the Lagrange problem is presented.

MSC:

49N45 Inverse problems in optimal control
49J15 Existence theories for optimal control problems involving ordinary differential equations
47N10 Applications of operator theory in optimization, convex analysis, mathematical programming, economics
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Lakshmikantham, V.; Bainov, D. D.; Simeonov, P. S., Theory of Impulsive Differential Equations (1989), World Scientific: World Scientific Singapore · Zbl 0719.34002
[2] Zavalishchion, A., Impulsive dynamic systems and applications to mathematical economic, Dynamic System Appl., 3, 443-449 (1994)
[3] Ahmed, N. U., Some remarks on the dynamics of impulsive systems in Banach space, Mathematical Anal., 8, 261-274 (2001) · Zbl 0995.34050
[4] Ahmed, N. U., Systems governed by impulsive differential inclusions on Hilbert spaces, Nonlinear Anal., 45, 693-706 (2001) · Zbl 0995.34053
[5] Ahmed, N. U., Optimal impulsive control for impulsive systems in Banach space, Int. J. Differential Equations App., 1.1, 37-52 (2002) · Zbl 0959.49023
[6] Liu, X.; Willms, A., Stability analysis and applications to large scale impulsive system a new approach, Canadian Appl. Math. Quart., 3, 419-444 (1995) · Zbl 0849.34044
[7] Ahmed, N. U.; Teo, K. L.; Hou, S. H., Nonlinear impulsive systems on infinite dimensional spaces, Nonlinear Anal., 54, 907-925 (2003) · Zbl 1030.34056
[8] Li, X.; Yong, J., Optimal Control Theory for Infinite Dimensional Systems (1995), Birkhäuser: Birkhäuser Boston
[9] Xiang, X., Optimal control for a class of strongly nonlinear evolution equations with constraints, Nonlinear Anal., 47, 57-66 (2001) · Zbl 1042.49507
[10] Ahmed, N. U.; Xiang, X., Nonlinear uncertain systems and necessary conditions of optimality, SIAM J. Control Optim., 35, 1755-1772 (1997) · Zbl 0907.49014
[11] Zeidler, E., Nonlinear Functional Analysis and Its Applications (1990), Springer-Verlag: Springer-Verlag New York
[12] Yosida, K., Functional Analysis (1995), Springer-Verlag: Springer-Verlag Berlin · Zbl 0152.32102
[13] Aubin, J. P.; Frankowska, H., Set-Valued Analysis (1990), Birkhäuser: Birkhäuser Boston, MA
[14] Liu, J. H., Nonlinear impulsive evolution equation, Dyn. Cont. Discrete and Impulsive System, 6, 1, 77-85 (1999) · Zbl 0932.34067
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.