Schauder's fixed-point theorem in nonlinear controllability problems

Control and Cybernetics

Volumn 29, Issue 1, 2000, Pages 152-165

  Klamka, J ^a  

^a SILESIAN UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

Continuous time systems; Controllability; Fixed point theorems; Nonlinear control systems; Schauder's fixed point theorem

Indexed keywords

EID: 0347093230     PISSN: 03248569     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (50)

1. BALACHANDRAN, K. (1985) Global and local controllability of nonlinear systems. Control Theory and Applications, 132, 14-17.
2. BALACHANDRAN, K. (1988) Controllability of a class of perturbed nonlinear systems. Kybernetika, 24, 61-64.
3. BALACHANDRAN K., AND BALASUBRAMANIAM P. (1994) Controllability of semilinear delay systems. Kybernetika, 30, 517-524.
4. BALACHANDRAN K., AND DAUER J.P. (1987) Controllability of nonlinear systems via fixed point theorems. Journal of Optimization Theory and Applications, 53, 345-352.
5. BALACHANDRAN K., AND DAUER J.P. (1989) Relative controllability of perturbations of nonlinear systems. Journal of Optimization Theory and Applications, 63, 51-56.
6. BALACHANDRAN K., AND DAUER J.P. (1990) Null controllability of nonlinear infinite delay systems with distributed delays in control. Journal Mathematical Analysis and Applications, 145, 274-281.
7. BALACHANDRAN K., AND DAUER J.P. (1993) Relative controllability of general nonlinear systems. Differential Equations and Dynamical Systems, 1, 119-122.
8. BALACHANDRAN K., AND DAUER J.P. (1996) Null controllability of nonlinear infinite delay systems with time varying multiple delays in control. Applied Mathematics Letters, 9, 115-121.
9. BALACHANDRAN K., AND DAUER J.P. (1998) Local controlability of semilinear evolution systems in Banach spaces. Indian Journal of Pure and Applied Mathematics, 29, 311-320.
10. BALACHANDRAN K., AND SOMASUNDARAM D. (1983) Controllability of a class of nonlinear systems with distributed delays in control. Kybernetika, 20, 475-482.
11. BALACHANDRAN K., AND SOMASUNDARAM D. (1985) Relative controllability of nonlinear systems with time varying delays in control. Kybernetika, 21, 65-72.
12. BALACHANDRAN K., DAUER J.P., AND BALASUBRAMANIAM P. (1995) Controllability of nonlinear integrodifferential systems in Banach spaces. Journal of Optimization Theory and Applications, 84, 83-91.
13. BALACHANDRAN K., PARK J.Y., AND ANTHONI S.M. (1999) Controllability of second order semilinear Volterra integrodifferential systems in Banach spaces. Bulletin of the Korean Mathematical Society, 36, 1-13.
14. CARMICHAEL N., AND QUINN M.D. (1988) Fixed-point methods in nonlinear control. IMA Journal of Mathematical Control and Information, 5, 41-67.
15. DANNON V.C., AND KARTSATOS A.G. (1987) The controllability of a quasi-linear functional differential system. Annales Polonici Mathematici, 47, 371-380.
16. DAUER J.P. (1972) A controllability technique for nonlinear systems. Journal of Mathematical Analysis and Applications, 37, 442-451.
17. DAUER J.P. (1976) Nonlinear perturbations of quasilinear control systems. Journal of Mathematical Analysis and Applications, 54, 717-725.
18. DAUER J.P., AND BALACHANDRAN K. (1997) Sample controllability of general nonlinear stochastic systems. Libertas Mathematica, 17, 143-153.
19. DAUER J.P., BALACHANDRAN K., AND ANTHONI S.M. (1998) Null controllability of nonlinear infinite neutral systems with delays in control. Computers Mathematical Applications, 36, 39-50.
20. DAVISON E. J., AND BALL D. (1972) On the global controllability of perturbed controllable systems. IEEE Transactions on Automatic Control, AC-17, 825-826.
21. DAVISON E.J., AND KUNZE E.C. (1970) Some sufficient conditions for the global and local controllability of nonlinear time varying systems. SIAM Journal on Control, 8, 489-497.
22. DEO S.G., AND SIVASUNDARAM S. (1997) Controllability of nonlinear integrodifferential systems. Control Theory Methods and Applications, 5, 171-178.
23. DO V.N. (1990) Controllability of semilinear systems. Journal of Optimization Theory and Applications, 65, 41-52.
24. EKE A.N. (1990) Total controllability for nonlinear perturbed systems. Journal of the Institute of Mathematical and Computer Sciences, 3, 335-340.
25. JOSHI M.C., AND GEORGE R.K. (1989) Controllability of nonlinear systems. Numerical Functional Analysis and Optimization, 10, 139-166.
26. JOSHI M.C., AND GEORGE R.K. (1992) On the controllability of predator-prey systems. Journal of Optimization Theory and Applications, 74, 243-258.
27. KLAMKA J. (1975A) On the global controllability of perturbed nonlinear systems. IEEE Transactions on Automatic Control, AC-20, 170-172.
28. KLAMKA J. (1975B) On the local controllability of perturbed nonlinear systems. IEEE Transactions on Automatic Control, AC-20, 289-291.
29. KLAMKA J. (1975c) Controllability of nonlinear systems with delay in control. IEEE Transactions on Automatic Control, AC-20, 702-704.
30. KLAMKA J. (1976) Relative controllability of nonlinear systems with delays in control. Automatica, 12, 633-634.
31. KLAMKA J. (1978) Relative controllability of nonlinear systems with distributed delays in control. International Journal of Control, 28, 307-312.
32. KLAMKA J. (1980) Controllability of nonlinear systems with distributed delays in control. International Journal of Control, 31, 811-819.
33. KLAMKA J. (1991A) Controllability of Dynamical Systems. Kluver Academic Publishers, Dordrecht, The Netherlands.
34. KLAMKA J. (1991B) Controllability of nonlinear systems with application to analysis of population dynamics. In: O. Arino, Mathematical Population Dynamics, ed., Marcel Dekker Inc. New York, 15, 217-221.
35. KLAMKA J. (1993) Controllability of dynamical systems - a survey. Archives of Control Sciences, 2, 281-307.
36. KLAMKA J. (1994) Controllability of nonlinear models arising in modelling of population dynamics. Applied Mathematics and Computer Science, 4, 203-209.
37. KLAMKA J. (1995) Constrained controllability of semilinear systems. IMA Journal of Mathematical Control and Information, 12, 245-252.
38. KLAMKA J. (1996) Constrained controllability of nonlinear systems. Journal of Mathematical Analysis and Applications, 201, 365-374.
39. KLAMKA J. (1998) Controllability of second-order semilinear infinite-dimensional dynamical systems. Applied Mathematics and Computer Science, 8, 459-470.
40. KLAMKA J. (1999A) Constrained controllability of semilinear systems. Preprints of 14 World Congress of IFAC, Pekin, 5-9.07.1999, B, 389-394.
41. KLAMKA J. (1999B) Controllability of semilinear systems with delays in control. Preprints of IEEE SMC'99 International Conference on Systems, Man and Cybernetics, Tokio, 12-15.10.1999, 253-258.
42. LUKES D.L. (1972) Global controllability of nonlinear systems. SIAM Journal on Control, 10, 112-126.
43. MAGNUSSON K., PRITCHARD A. J., AND QUINN M.D. (1985) The application of fixed-point theorems to global nonlinear controllability problems. Mathematical Control Theory. Banach Center Publications. Polish Scientific Publishers. Warsaw, 14, 319-344.
44. MIRZA K., AND WOMACK B.F. (1972) On the controllability of a class of nonlinear systems. IEEE Transactions on Automatic Control, AC-17, 531-535.
45. MIRZA K., AND WOMACK B.F. (1972) On the controllability of nonlinear time-delay systems. IEEE Transactions on Automatic Control, AC-17, 812-814.
46. ONWUATU J.U. (1989) On controllability of nonlinear systems with distributed delays in the control. Indian Journal of Pure and Applied Mathematics, 20, 213-228.
47. ONWUATU J.U. (1993) Null controllability of nonlinear infinite neutral system. Kybernetika, 29, 325-336.
48. PARK J.Y., AND HAN H.K. (1997) Controllability for some second order differential equations. Bulletin of the Korean Mathematical Society, 34, 411-419.
49. WEI K.C. (1976) A class of controllable nonlinear systems. IEEE Transactions on Automatic Control, AC-21, 787-789.
50. YAMAMOTO Y. (1977) Controllability of nonlinear systems. Journal of Optimization Theory and Applications, 22, 41-49.