Control and optimal response problems for quasilinear impulsive integrodifferential equations

European Journal of Operational Research

Volumn 169, Issue 3, 2006, Pages 1128-1147

  Akhmet, M U ^a   Kirane, M ^b   Tleubergenova, M A ^c   Weber, G W ^a  

^a MIDDLE EAST TECHNICAL UNIVERSITY   (Turkey)

^b UNIVERSITÉ DE LA ROCHELLE   (France)

^c SATBAYEV UNIVERSITY   (Kazakhstan)

Author keywords

Control; Impulse; Integrodifferential equation; Linear programming; Optimal control of response; Quasilinear system

Indexed keywords

INTEGRODIFFERENTIAL EQUATIONS; LINEAR PROGRAMMING; LINEAR SYSTEMS; OPTIMAL CONTROL SYSTEMS;

IMPULSE; INTEGRODIFFERENTIAL EQUATION; QUASILINEAR SYSTEM;

OPERATIONS RESEARCH;

EID: 27144458449     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ejor.2004.10.030     Document Type: Conference Paper

References (39)

1. M.U. Akhmet, J. Gebert, H. Öktem, S.W. Pickl, and G.-W. Weber An improved method for analytical modeling and anticipation of gene expression patterns Journal of Computational Technologies 4 2005 (cf. also www.iam.metu.edu.tr/research/preprint/6f.pdf )
2. M.U. Akhmetov, and N.A. Perestyuk On comparison method for differential systems with pulse effect Differential Equations 9 26 1990 1079 1086
3. M.U. Akhmetov, and N.A. Perestyuk Periodic and almost periodic solutions of integro-differential equations with impulse actions Matematicheskaya Fizika i Nelineinaya Mekhanika 42 1987 5 9
4. M.U. Akhmetov, N.A. Perestyuk, and M.A. Tleubergenova The control of linear impulsive systems Ukrainskii Matematicheskii Zhurnal 47 1995 307 314
5. M. Akhmetov, and R. Sejilova The control of the boundary value problem for linear impulsive integrodifferential systems Journal of Mathematical Analysis and Applications 236 1999 312 326
6. M.U. Akhmetov, and A. Zafer The controllability of boundary-value problems for quasilinear impulsive systems Nonlinear Analysis 34 1998 1055 1065
7. L. Anokhin, L. Berezansky, and E. Braverman Stability of linear delay impulsive differential equations Dynamic Systems and Applications 4 1995 173 188
8. A.A. Aslanyan Conditions for optimum in problems of control of impulsive systems Akademiya Nauk Ukrainskoi SSR Doklady, Seriya A 11 1982 3 6
9. K. Balachandran, and D. Lalitha Controllability of nonlinear Volterra integro-differential systems with prescribed controls Journal of Applied Mathematics and Stochastic Analysis 5 1992 139 146
10. B. Ballobás, and A.G. Thomason Threshold functions Combinatorica 7 1987 35 38
11. R. Bellman Mathematical Methods in Medicine 1983 World Scientific Singapore
12. A. Bensoussan, and J.L. Lions Nouvelle formulation de problèmes de contrôle impulsionnel et applications Comptes Rendus de l Academie des Sciences Paris 276 1973 1182 1189
13. C. Corduneanu Sur une equation integrale de la théorie du réglage automatique Comptes Rendus de l Academie des Sciences Paris 256 1967 3564 3567
14. A.L. Dontchev, W.W. Hager, A.B. Poore, and B. Yang Optimality, stability, and convergence in nonlinear control Applied Mathematics and Optimization 31 1995 297 326
15. P. Erdös, and A. Rényi On the evolution of random graphs Publ. Math. Inst. Hungar. Acad. Sci 5 1960 17 61
16. T. Ergenc, S.W. Pickl, N. Radde, G.-W. Weber, On the topology of generalized semi-infinite optimization and anticipatory systems, International Journal Computing Anticipatory Systems 14-16 (2004).
17. J. Gebert, M. Lätsch, S.W. Pickl, G.-W. Weber, R. Wünschiers, An algorithm to analyze stability of gene-expression patterns, Discrete Mathematics and Data Mining of Discrete Applied Mathematics (special issue), E. Boros, P.L. Hammer, A. Kogan (guest editors), in press.
18. J. Gebert, H. Öktem, S.W. Pickl, N. Radde, G.-W. Weber, F.B. Yilmaz, Inference of gene expression patterns by using a hybrid system formulation-an algorithmic approach to local state transition matrices, in: Proceedings of IIAS (International Institute for Advanced Studies), 16th International Symposium for Anticipatory and Predictive Systems, Baden Baden, July-August 2004 (cf. also www.iam.metu.edu.tr/research/preprint/20f.pdf ).
19. J. Gebert, N. Radde, Modelling gene regulatory networks with piecewise linear differential equations, preprint, Center of Applied Computer Science, University of Cologne, and talks held at EURO Summer Institute "Optimization and Data Mining", Ankara, Turkey, July 9-25, 2004. Available from: .
20. J. Guckenheimer, and P. Holmes Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields 1983 Springer-Verlag New York
21. A. Halanay, and D. Wexler Qualitative Theory of Impulse Systems 1968 Editura Academiei Republici Socialiste Romania Bucuresti
22. M. Hestenes Calculus of Variations and Optimal Control Theory 1966 John Wiley New York
23. K.H. Hofmann, Analysis I, An Introduction to Mathematics via Analysis, Berliner Studienreihen zur Mathematik 8, Heldermann Verlag, Lemgo, 2000.
24. L.V. Kantorovich, and G.P. Akilov Functional Analysis 1982 Pergamon Press Oxford
25. A. Kaplan, and R. Tichatschke On a class of terminal variational problems J. Guddat H.Th. Jongen F. Nozicka G. Still F. Twilt Parametric Optimization and Related Topics IV 1996 Peter Lang Frankfurt, Berlin, New York 185 199
26. A. Kaplan, and R. Tichatschke On the numerical treatment of a class of semi-infinite terminal problems Optimization 41 1997 1 36
27. W. Krabs, On time-minimal heating or cooling of a ball, International Series of Numerical Mathematics 81, Birkhäuser, Basel, 1987, pp. 121-131.
28. E. Kropat, S. Pickl, A. Rößler, and G.-W. Weber A new algorithm from semi-infinite optimization for a problem of time-minimal control Journal of Computational Technologies 5 4 2000 67 81
29. E. Kropat, S. Pickl, A. Rößler, G.-W. Weber, On theoretical and practical relations between discrete optimization and nonlinear optimization, Colloquy Optimization-Structure and Stability of Dynamical Systems of Journal of Computational Technologies 7 (2002) 27-62 (special issue).
30. V. Lakshmikantham, D.D. Bainov, and P.S. Simeonov Theory of Impulsive Differential Equations 1989 World Scientific Singapore, New York
31. E.B. Lee, and L. Markus Foundations of Optimal Control Theory 1967 John Wiley New York
32. K. Malanowski Regularity of solutions in stability analysis of optimization and optimal control problems Control and Cybernetics 23 1994 61 86
33. K. Malanowski, and H. Maurer Sensitivity analysis for parametric control problems with control-state constraints Computational Optimization Applications 5 1996 253 283
34. L.S. Pontryagin, V.G. Boltyanskii, R.V. Gamkrelidze, and E.F. Mishchenko The Mathematical Theory of Optimal Processes 1962 Interscience Publishers, John Wiley New York
35. A.M. Samoilenko, and N.A. Perestyuk Impulsive Differential Equations 1995 World Scientific Singapore
36. S. Sivasundram Controllability and observability of nonlinear integro-differential systems Proceedings of Dynamic Systems and Applications 2 1996 507 516
37. G.-W. Weber Generalized Semi-infinite Optimization and Related Topics 2003 Heldermann Verlag Lemgo
38. G.-W. Weber Generalized semi-infinite optimization: Theory and applications in optimal control and discrete optimization Journal of Statistics & Management Systems 5 1-3 2002 359 388
39. G.-W. Weber, New projects at the Institute of Applied Mathematics in METU, talk held at Workshop on advances in continuous optimization, Istanbul, Turkey, July 4-5, 2003.