Approximate controllability of semilinear deterministic and stochastic evolution equations in abstract spaces

SIAM Journal on Control and Optimization

Volumn 42, Issue 5, 2003, Pages 1604-1622

  Mahmudov, Nazim I ^a  

^a EASTERN MEDITERRANEAN UNIVERSITY   (Turkey)

Author keywords

Controllability; Semilinear evolution equations; Stochastic evolution equations; Symmetric operators; The contraction mapping principle; The schauder fixed point theorem

Indexed keywords

SEMILINEAR EVOLUTION EQUATIONS; STOCHASTIC EVOLUTION EQUATIONS; SYMMETRIC OPERATORS;

MAPPING; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; STOCHASTIC CONTROL SYSTEMS; THEOREM PROVING;

LINEAR SYSTEMS;

EID: 4944255103     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0363012901391688     Document Type: Article

References (36)

1. N. U. AHMED AND S. KERBAL, On approximate controllability for semilinear systems, Nonlinear World, 2 (1995), pp. 53-67.
2. K. BALACHANDRAN, P. BALASUBRAMANIAM, AND J. P. DAUER, Controllability of nonlinear integrodifferential systems in Banach space, J. Optim. Theory Appl., 84 (1995), pp. 83-91.
3. K. BALACHANDRAN AND J. P. DAUER, Controllability of nonlinear systems via fixed-point theorems, J. Optim. Theory Appl., 53 (1987), pp. 345-352.
4. V. BARBU AND G. TESSITORE, Considerations on the controllability of stochastic linear heat equations, in Stochastic Partial Differential Equations and Applications, Lecture Notes in Pure and Appl. Math. 227, G. Da Prato and L. Tubaro, eds., Marcel Dekker, New York, 2002, pp. 39-51.
5. V. BARBU AND TH. PRECUPANU, Convexity and Optimization in Banach Spaces, 2nd ed., Mathematics and Its Applications (East European Series) 10, D. Reidel Publishing Co., Dordrecht, The Netherlands, 1986.
6. A. E. BASHIROV AND N. I. MAHMUDOV, On concepts of controllability for linear deterministic and stochastic systems, SIAM J. Control Optim., 37 (1999), pp. 1808-1821.
7. W. BIAN, Approximate controllability for semilinear systems, Acta Math. Hungar., 81 (1998), pp. 41-57.
8. W. C. CHEWNING AND T. I. SEIDMAN, A convergent scheme for boundary control of the heat equation, SIAM J. Control Optim., 15 (1977), pp. 64-72.
9. E. N. CHUCKWU AND S. M. LENHART, Controllability questions for nonlinear systems in abstract spaces, J. Optim. Theory Appl., 68 (1991), pp. 437-462.
10. R. F. CURTAIN AND H. J. ZWART, An Introduction to Infinite-Dimensional Linear Systems Theory, Springer-Verlag, New York, 1992.
11. G. DA PRATO AND J. ZABCZYK, Stochastic Equations in Infinite Dimensions, Encyclopedia Math. Appl. 44, Cambridge University Press, Cambridge, UK, 1992.
12. M. A. DUBOV AND B. S. MORDUKHOVICH, Theory of controllability of linear stochastic systems, Differ. Eq., 14 (1978), pp. 1609-1612.
13. V. N. Do, Controllability of semilinear systems, J. Optim. Theory Appl., 65 (1990), pp. 41-52.
14. C. FABRE, J. P. PUEL, AND E. ZUAZUA, Approximate controllability of the semilinear heat equation, Proc. Roy. Soc. Edinburgh Sect. A 125 (1995), pp. 31-61.
15. H. O. FATTORINI, On complete controllability of linear systems, J. Differential Equations, 3 (1967), pp. 391-402.
16. L. A. FERNANDEZ AND E. ZUAZUA, Approximate controllability for semilinear heat equation involving gradient terms, J. Optim. Theory Appl., 101 (1999), pp. 307-328.
17. E. FERNANDEZ-CARA, Null controllability of the semilinear heat equation, ESAIM Control Optim. Calc. Var., 2 (1997), pp. 87-103.
18. R. K. GEORGE, Approximate controllability of nonautonomous semilinear systems, Nonlinear Anal., 24 (1995), pp. 1377-1393.
19. O. YU. IMANUVILOV, Boundary controllability of parabolic equations, Sb. Math., 186 (1995), pp. 879-900.
20. A. YU. KHAPALOV, Approximate controllability properties of the semilinear heat equation with lumped controls, Int. J. Appl. Math. Comput. Sci., 9 (1999), pp. 751-765.
21. J. KLAMKA, Schauder's fixed-point theorem in nonlinear controllability problems, Control Cybernet., 29 (2000), pp. 153-165.
22. I. LASIECKA AND R. TRIGGIANI, Control theory for partial differential equations: Continuous and approximation theories II, in Abstract Hyperbolic-Like Systems over a Finite Time Horizon, Encyclopedia Math. Appl. 75, Cambridge University Press, Cambridge, UK, 2000, pp. i-xii, 645-1067, 11-14.
23. N. I. MAHMUDOV, Controllability of linear stochastic systems, IEEE Trans. Automat. Control, 46 (2001), pp. 724-731.
24. N. I. MAHMUDOV, Controllability of linear stochastic systems in Hilbert spaces, J. Math. Anal. Appl., 259 (2001), pp. 64-82.
25. S. NAKAGIRI AND M. YAMAMOTO, Controllability and observability of linear retarded systems in Banach space, Internat. J. Control, 49 (1989), pp. 1489-1504.
26. K. NAITO, Controllability of semilinear control systems dominated by the linear part, SIAM J. Control Optim., 25 (1987), pp. 715-722.
27. A. PAZY, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983.
28. T. I. SEIDMAN, Invariance of the reachable set under nonlinear perturbations, SIAM J. Control Optim., 25 (1987), pp. 1173-1191.
29. R. E. SHOWALTER, Monotone Operators in Banach Space and Nonlinear Partial Differential Equations, AMS, Providence, RI, 1997.
30. M. SIRBU AND G. TESSITORE, Null controllability of an infinite dimensional SDE with state and control-dependent noise, Systems Control Lett., 44 (2001), pp. 385-394.
31. R. TRIGGIANI, Controllability and observability in Banach space with bounded operators, SIAM J. Control, 13 (1975), pp. 462-491.
32. H. H. VAHANIYA, V. I. TARIELADZE, AND C. A. CHOBANIAN, Probability Distributions in Banach Spaces, Nauka, Moscow, 1985 (in Russian).
33. M. YAMAMOTO AND J. Y. PARK, Controllability for parabolic equations with uniformly bounded nonlinear terms, J. Optim. Theory Appl., 66 (1990), pp. 515-532.
34. X. LI AND J. YONG, Optimal Control Theory for Infinite Dimensional Systems, Birkhäuser Boston, Boston, 1995.
35. H. X. ZHOU, Approximate controllability for a class of semilinear abstract equations, SIAM J. Control Optim., 21 (1983), pp. 551-565.
36. E. ZUAZUA, Controllability of partial differential equations and its semi-discrete approximations, Discrete Contin. Dyn. Syst., 8 (2002), pp. 469-513.