Abstract
This article presents a survey of papers published on controllability of nonlinear systems, including nonlinear delay systems, by means of fixed-point principles.
Similar content being viewed by others
References
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.
Dauer, J. P.,A Controllability Technique for Nonlinear Systems, Journal of Mathematical Analysis and Applications, Vol. 37, pp. 442–451, 1972.
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.
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.
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.
Klamka, J.,On the Global Controllability of Perturbed Nonlinear Systems, IEEE Transactions on Automatic Control, Vol. AC-20, pp. 170–172, 1975.
Klamka, J.,On the Local Controllability of Perturbed Nonlinear Systems, IEEE Transactions on Automatic Control, Vol. AC-20, pp. 289–291, 1975.
Lukes, D. L.,Global Controllability of Disturbed Nonlinear Equations, SIAM Journal on Control, Vol. 12, pp. 695–704, 1974.
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.
Wei, K. C.,A Class of Controllable Nonlinear Systems, IEEE Transactions on Automatic Control, Vol. AC-21, pp. 787–789, 1976.
Klamka, J.,Controllability of Nonlinear Systems with Delay in Control, IEEE Transactions on Automatic Control, Vol. AC-20, pp. 702–704, 1975.
Klamka, J.,Relative Controllability of Nonlinear Systems with Delays in Control, Automatica, Vol. 12, pp. 633–634, 1976.
Klamka, J.,Relative Controllability of Nonlinear Systems with Distributed Delays in Control, International Journal of Control, Vol. 28, pp. 307–312, 1978.
Klamka, J.,Controllability of Nonlinear Systems with Distributed Delays in Control, International Journal of Control, Vol. 31, pp. 811–819, 1980.
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.
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.
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.
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.
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.
Lukes, D. L.,Global Controllability of Nonlinear Systems, SIAM Journal on Control, Vol. 10, pp. 112–126, 1972; Erratum, Vol. 11, p. 186, 1973.
Vidyasager, M.,A Controllability Condition for Nonlinear Systems, IEEE Transactions on Automatic Control, Vol. AC-17, pp. 569–570, 1972.
Dauer, J. P.,Nonlinear Perturbations of Quasi-Linear Control Systems, Journal of Mathematical Analysis and Applications, Vol. 54, pp. 717–725, 1976.
Dauer, J. P.,Controllability of Perturbed Nonlinear Systems, Rendiconti della Accademia Nazionale dei Lincei, Serie 8, Vol. 63, pp. 345–350, 1977.
Kartsatos, A. G.,Global Controllability of Perturbed Quasi-Linear Systems, Problems of Control and Information Theory, Vol. 3, pp. 137–145, 1974.
Dauer, J. P., andGahl, R. D.,Controllability of Nonlinear Delay Systems, Journal of Optimization Theory and Applications, Vol. 21, pp. 59–70, 1977.
Balachandran, K.,Controllability of Nonlinear Perturbations of Linear Systems with Distributed Delays in Control, Robotica, Vol. 3, pp. 89–91, 1985.
Yamamoto, Y.,Controllability of Nonlinear Systems, Journal of Optimization Theory and Applications, Vol. 22, pp. 41–49, 1977.
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.
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.
Anichini, G.,Global Controllability of Nonlinear Control Processes with Prescribed Controls, Journal of Optimization Theory and Applications, Vol. 32, pp. 183–199, 1980.
Anichini, G.,Controllability and Controllability with Prescribed Controls, Journal of Optimization Theory and Applications, Vol. 39, pp. 34–45, 1983.
Dauer, J. P.,Controllability of Nonlinear Systems with Restrained Controls, Journal of Optimization Theory and Applications, Vol. 14, pp. 251–262, 1974.
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.
Chukwu, E. N.,Controllability of Delay Systems with Restrained Controls, Journal of Optimization Theory and Applications, Vol. 29, pp. 301–320, 1979.
Chukwu, E. N.,Total Controllability to Affine Manifolds of Control Systems, Journal of Optimization Theory and Applications, Vol. 42, pp. 181–199, 1984.
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.
Dacka, C.,On the Controllability of a Class of Nonlinear Systems, IEEE Transactions on Automatic Control, Vol. AC-25, pp. 263–266, 1980.
Dacka, C.,On the Controllability of Perturbed Nonlinear Systems, Podstawy Sterowania, Vol. 10, pp. 335–348, 1980.
Dacka, C.,On the Controllability of Certain Nonlinear Systems, Archiwum Automatyki i Telemechaniki, Vol. 25, pp. 483–494, 1980.
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.
Dacka, C.,On the Controllability of Nonlinear Systems with Time-Variable Delays, IEEE Transactions on Automatic Control, Vol. AC-26, pp. 956–959, 1981.
Balachandran, K., andSomasundaram, D.,Controllability of a Class of Nonlinear Systems with Distributed Delays in Control, Kybernetika, Vol. 19, pp. 475–482, 1983.
Balachandran, K., andSomasundaram, D.,Relative Controllability of Nonlinear Systems with Time Varying Delays in Control, Kybernetika, Vol. 21, pp. 65–72, 1985.
Dacka, C.,Relative Controllability of Perturbed Nonlinear Systems with Delay in Control, IEEE Transactions on Automatic Control, Vol. AC-27, pp. 268–270, 1982.
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.
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.
Gahl, R. D.,Controllability of Nonlinear Systems of Neutral Type, Journal of Mathematical Analysis and Applications, Vol. 63, pp. 33–42, 1978.
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.
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.
Angell, T. S.,The Controllability Problem for Nonlinear Volterra Systems, Journal of Optimization Theory and Applications, Vol. 41, pp. 9–35, 1983.
Author information
Authors and Affiliations
Additional information
Communicated by G. Leitmann
Rights and permissions
About this article
Cite this article
Balachandran, K., Dauer, J.P. Controllability of nonlinear systems via fixed-point theorems. J Optim Theory Appl 53, 345–352 (1987). https://doi.org/10.1007/BF00938943
Issue Date:
DOI: https://doi.org/10.1007/BF00938943