×
Balachandran, K.; Dauer, J. P.

Controllability of nonlinear systems via fixed-point theorems. (English) Zbl 0596.93010

J. Optimization Theory Appl. 53, 345-352 (1987).
This article presents a survey of papers published on controllability of nonlinear systems, including nonlinear delay systems, by means of fixed- point principles.

Cited in 1 Review
Cited in 55 Documents

MSC:

93B05 Controllability
47H10 Fixed-point theorems
93C10 Nonlinear systems in control theory
93B03 Attainable sets, reachability
34K35 Control problems for functional-differential equations

Keywords:

controllability of nonlinear systems; nonlinear delay systems; fixed- point principles
PDF BibTeX XML Cite
\textit{K. Balachandran} and \textit{J. P. Dauer}, J. Optim. Theory Appl. 53, 345--352 (1987; Zbl 0596.93010)
Full Text: DOI
  • logo of hbz
  • logo of WorldCat

References:

[1] Tarnove, I.,A Controllability Problem for Nonlinear Systems, Mathematical Theory of Control, Edited by A. V. Balakrishnan and L. W. Neustadt, Academic Press, New York, New York, pp. 170-179, 1967. · Zbl 0214.40603
[2] Dauer, J. P.,A Controllability Technique for Nonlinear Systems, Journal of Mathematical Analysis and Applications, Vol. 37, pp. 442-451, 1972. · Zbl 0224.93006
[3] Mirza, K. B., andWomack, B.,On the Controllability of a Class of Nonlinear Systems, IEEE Transactions on Automatic Control, Vol. AC-16, pp. 497-498, 1971.
[4] Davison, E. J., andKunze, E. G.,Some Sufficient Conditions for the Global and Local Controllability of Nonlinear Time Varying Systems, SIAM Journal on Control, Vol. 8, pp. 489-497, 1970. · Zbl 0236.93007
[5] Davison, E. J., andBall, D.,On the Global Controllability of Perturbed Controllable Systems, IEEE Transactions on Automatic Control, Vol. AC-17, pp. 825-826, 1972. · Zbl 0265.93003
[6] Klamka, J.,On the Global Controllability of Perturbed Nonlinear Systems, IEEE Transactions on Automatic Control, Vol. AC-20, pp. 170-172, 1975. · Zbl 0299.93007
[7] Klamka, J.,On the Local Controllability of Perturbed Nonlinear Systems, IEEE Transactions on Automatic Control, Vol. AC-20, pp. 289-291, 1975. · Zbl 0299.93006
[8] Lukes, D. L.,Global Controllability of Disturbed Nonlinear Equations, SIAM Journal on Control, Vol. 12, pp. 695-704, 1974. · Zbl 0289.93009
[9] Mirza, K. B., andWomack, B. F.,On the Controllability of a Class of Nonlinear Systems, IEEE Transactions on Automatic Control, Vol. AC-17, pp. 531-535, 1972. · Zbl 0259.93004
[10] Wei, K. C.,A Class of Controllable Nonlinear Systems, IEEE Transactions on Automatic Control, Vol. AC-21, pp. 787-789, 1976. · Zbl 0334.93010
[11] Klamka, J.,Controllability of Nonlinear Systems with Delay in Control, IEEE Transactions on Automatic Control, Vol. AC-20, pp. 702-704, 1975. · Zbl 0319.93011
[12] Klamka, J.,Relative Controllability of Nonlinear Systems with Delays in Control, Automatica, Vol. 12, pp. 633-634, 1976. · Zbl 0345.93014
[13] Klamka, J.,Relative Controllability of Nonlinear Systems with Distributed Delays in Control, International Journal of Control, Vol. 28, pp. 307-312, 1978. · Zbl 0402.93012
[14] Klamka, J.,Controllability of Nonlinear Systems with Distributed Delays in Control, International Journal of Control, Vol. 31, pp. 811-819, 1980. · Zbl 0462.93009
[15] Klamka, J.,Controllability of Nonlinear Systems with Delays in Control, First International Conference on Functional Differential Systems and Related Topics, Edited by M. Kisielewicz, Higher College of Engineering, Zielona Gora, Poland, pp. 168-178, 1981.
[16] Wei, K. C., andPearson, A. E.,Global Controllability for a Class of Bilinear Systems, IEEE Transactions on Automatic Control, Vol. AC-23, pp. 486-488, 1978. · Zbl 0397.93005
[17] Balachandran, K., andSomasundaram, D.,Controllability of Nonlinear Systems Consisting of a Bilinear Mode with Time Varying Delays in Control, Automatica, Vol. 20, pp. 257-258, 1984. · Zbl 0535.93006
[18] Somasundaram, D., andBalachandran, K.,Controllability of Nonlinear Systems Consisting of a Bilinear Mode with Distributed Delays in Control, IEEE Transactions on Automatic Control, Vol. AC-29, pp. 573-575, 1984. · Zbl 0542.93008
[19] Mirza, K. B., andWomack, B. F.,On the Controllability of Nonlinear Time-Delay Systems, IEEE Transactions on Automatic Control, Vol. AC-17, pp. 812-814, 1972. · Zbl 0261.93005
[20] Lukes, D. L.,Global Controllability of Nonlinear Systems, SIAM Journal on Control, Vol. 10, pp. 112-126, 1972; Erratum, Vol. 11, p. 186, 1973. · Zbl 0264.93004
[21] Vidyasager, M.,A Controllability Condition for Nonlinear Systems, IEEE Transactions on Automatic Control, Vol. AC-17, pp. 569-570, 1972. · Zbl 0262.93008
[22] Dauer, J. P.,Nonlinear Perturbations of Quasi-Linear Control Systems, Journal of Mathematical Analysis and Applications, Vol. 54, pp. 717-725, 1976. · Zbl 0339.93004
[23] Dauer, J. P.,Controllability of Perturbed Nonlinear Systems, Rendiconti della Accademia Nazionale dei Lincei, Serie 8, Vol. 63, pp. 345-350, 1977. · Zbl 0413.93012
[24] Kartsatos, A. G.,Global Controllability of Perturbed Quasi-Linear Systems, Problems of Control and Information Theory, Vol. 3, pp. 137-145, 1974. · Zbl 0303.93014
[25] Dauer, J. P., andGahl, R. D.,Controllability of Nonlinear Delay Systems, Journal of Optimization Theory and Applications, Vol. 21, pp. 59-70, 1977. · Zbl 0325.93007
[26] Balachandran, K.,Controllability of Nonlinear Perturbations of Linear Systems with Distributed Delays in Control, Robotica, Vol. 3, pp. 89-91, 1985.
[27] Yamamoto, Y.,Controllability of Nonlinear Systems, Journal of Optimization Theory and Applications, Vol. 22, pp. 41-49, 1977. · Zbl 0336.93009
[28] Khanh, V. U.,Global Controllability of General Nonlinear Systems, Second International Conference on Functional Differential Systems and Related Topics, Edited by M. Kisielewicz, Higher College of Engineering, Zielona Gora, Poland, pp. 156-163, 1981.
[29] Johnson, H. H., andMilbourn, A. J.,Null Controllabilty for Nonlinear Systems of the form y=A(t)y(t)+B(t)u y (t)+f(y, u y,t), Recent Theoretical Developments in Control, Edited by M. J. Gregson, Academic Press, New York, pp. 337-350, 1978.
[30] Anichini, G.,Global Controllability of Nonlinear Control Processes with Prescribed Controls, Journal of Optimization Theory and Applications, Vol. 32, pp. 183-199, 1980. · Zbl 0417.93016
[31] Anichini, G.,Controllability and Controllability with Prescribed Controls, Journal of Optimization Theory and Applications, Vol. 39, pp. 34-45, 1983. · Zbl 0479.93012
[32] Dauer, J. P.,Controllability of Nonlinear Systems with Restrained Controls, Journal of Optimization Theory and Applications, Vol. 14, pp. 251-262, 1974. · Zbl 0268.93005
[33] Chukwu, E. N., andSilliman, S. D.,Complete Controllability to a Closed Target Set, Journal of Optimization Theory and Applications, Vol. 21, pp. 369-383, 1977. · Zbl 0332.93016
[34] Chukwu, E. N.,Controllability of Delay Systems with Restrained Controls, Journal of Optimization Theory and Applications, Vol. 29, pp. 301-320, 1979. · Zbl 0387.93009
[35] Chukwu, E. N.,Total Controllability to Affine Manifolds of Control Systems, Journal of Optimization Theory and Applications, Vol. 42, pp. 181-199, 1984. · Zbl 0504.93012
[36] Chukwu, E. N.,Null Controllability in Function Space of Nonlinear Retarded Systems with Limited Controls, Journal of Mathematical Analysis and Applications, Vol. 103, pp. 198-210, 1984. · Zbl 0555.93008
[37] Dacka, C.,On the Controllability of a Class of Nonlinear Systems, IEEE Transactions on Automatic Control, Vol. AC-25, pp. 263-266, 1980. · Zbl 0439.93006
[38] Dacka, C.,On the Controllability of Perturbed Nonlinear Systems, Podstawy Sterowania, Vol. 10, pp. 335-348, 1980. · Zbl 0457.93015
[39] Dacka, C.,On the Controllability of Certain Nonlinear Systems, Archiwum Automatyki i Telemechaniki, Vol. 25, pp. 483-494, 1980. · Zbl 0457.93015
[40] Balachandran, K.,Global and Local Controllability of Nonlinear Systems, Proceedings of the IEE, Part D, Control Theory and Applications, Vol. 132, pp. 14-17, 1985. · Zbl 0554.93012
[41] Dacka, C.,On the Controllability of Nonlinear Systems with Time-Variable Delays, IEEE Transactions on Automatic Control, Vol. AC-26, pp. 956-959, 1981. · Zbl 0553.93007
[42] Balachandran, K., andSomasundaram, D.,Controllability of a Class of Nonlinear Systems with Distributed Delays in Control, Kybernetika, Vol. 19, pp. 475-482, 1983. · Zbl 0528.93012
[43] Balachandran, K., andSomasundaram, D.,Relative Controllability of Nonlinear Systems with Time Varying Delays in Control, Kybernetika, Vol. 21, pp. 65-72, 1985. · Zbl 0558.93008
[44] Dacka, C.,Relative Controllability of Perturbed Nonlinear Systems with Delay in Control, IEEE Transactions on Automatic Control, Vol. AC-27, pp. 268-270, 1982. · Zbl 0469.93021
[45] Somasundaram, D., andBalachandran, K.,Relative Controllability of a Class of Nonlinear Systems with Delay in Control, Indian Journal of Pure and Applied Mathematics, Vol. 14, pp. 1327-1334, 1983.
[46] Sastry, S. S., andDesoer, C. A.,The Robustness of Controllability and Observability of Linear Time Varying Systems, IEEE Transactions on Automatic Control, Vol. AC-27, pp. 933-939, 1982. · Zbl 0486.93013
[47] Gahl, R. D.,Controllability of Nonlinear Systems of Neutral Type, Journal of Mathematical Analysis and Applications, Vol. 63, pp. 33-42, 1978. · Zbl 0406.34052
[48] Chukwu, E. N.,Functional Inclusion and Controllability of Nonlinear Neutral Functional Differential Systems, Journal of Optimization Theory and Applications, Vol. 29, pp. 291-300, 1979. · Zbl 0416.93026
[49] Angell, T. S.,On Controllability for Nonlinear Hereditary Systems; A Fixed-Point Approach, Nonlinear Analysis Theory, Methods and Applications, Vol. 4, pp. 529-548, 1980. · Zbl 0453.93009
[50] Angell, T. S.,The Controllability Problem for Nonlinear Volterra Systems, Journal of Optimization Theory and Applications, Vol. 41, pp. 9-35, 1983. · Zbl 0497.93010
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.