×

Controllability of nonlinear integrodifferential systems in Banach space. (English) Zbl 0821.93010

Summary: Sufficient conditions for controllability of nonlinear integro- differential systems in a Banach space are established. The results are obtained using the Schauder fixed-point theorem.

MSC:

93B05 Controllability
93B28 Operator-theoretic methods
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
93C25 Control/observation systems in abstract spaces
93C10 Nonlinear systems in control theory
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Chukwu, E. N., andLenhart, S. M.,Controllability Questions for Nonlinear Systems in Abstract Spaces, Journal of Optimization Theory and Applications, Vol. 68, pp. 437–462, 1991. · Zbl 0697.49040 · doi:10.1007/BF00940064
[2] Nakagiri, S., andYamamoto, M.,Controllability and Observability of Linear Retarded Systems in Banach Spaces, International Journal of Control, Vol. 49, pp. 1489–1504, 1989. · Zbl 0676.93029
[3] Naito, K.,Controllability of Semilinear Control Systems Dominated by the Linear Part, SIAM Journal on Control and Optimization, Vol. 25, pp. 715–722, 1987. · Zbl 0617.93004 · doi:10.1137/0325040
[4] Naito, K.,Approximate Controllability for Trajectories of Semilinear Control Systems, Journal of Optimization Theory and Applications, Vol. 60, pp. 57–65, 1989. · Zbl 0632.93007 · doi:10.1007/BF00938799
[5] Naito, K.,On Controllability for a Nonlinear Volterra Equation, Nonlinear Analysis: Theory, Methods and Applications, Vol. 18, pp. 99–108, 1992. · Zbl 0768.93011 · doi:10.1016/0362-546X(92)90050-O
[6] Naito, K., andPark, J. Y.,Approximate Controllability for Trajectories of a Delay Volterra Control System, Journal of Optimization Theory and Applications, Vol. 61, pp. 271–279, 1989. · Zbl 0644.93009 · doi:10.1007/BF00962800
[7] Zhou, H. X.,Approximate Controllability for a Class of Semilinear Abstract Equations, SIAM Journal on Control and Optimization, Vol. 21, pp. 551–565, 1983. · Zbl 0516.93009 · doi:10.1137/0321033
[8] Triggiani, R.,Controllability, Observability, and Stabilizability of Dynamical Systems in Banach Space with Bounded Operators, PhD Thesis, University of Michigan, Ann Arbor, Michigan, 1973.
[9] Triggiani, R.,Controllability and Observability in Banach Spaces with Bounded Operators, SIAM Journal on Control, Vol. 13, pp. 462–491, 1975. · Zbl 0268.93007 · doi:10.1137/0313028
[10] Lasiecka, I., andTriggiani, R.,Exact Controllability of Semilinear Abstract Systems with Application to Waves and Plates Boundary Control Problems, Applications of Mathematical Optimization, Vol. 23, pp. 109–154, 1991. · Zbl 0729.93023 · doi:10.1007/BF01442394
[11] Quinn, M. D., andCarmichael, N.,An Approach to Nonlinear Control Problems Using Fixed-Point Methods, Degree Theory, and Pseudo-Inverses, Numerical Functional Analysis and Optimization, Vol. 7, pp. 197–219, 1984–1985. · Zbl 0563.93013 · doi:10.1080/01630568508816189
[12] Kwun, Y. C., Park, J. Y., andRyu, J. W.,Approximate Controllability and Controllability for Delay Volterra Systems, Bulletin of the Korean Mathematics Society, Vol. 28, pp. 131–145, 1991. · Zbl 0770.93009
[13] Nussbaum, R. P.,The Fixed-Point Index and Asymptotic Fixed-Point Theorems for k-Set Contractions, Bulletin of the American Mathematical Society, Vol. 75, pp. 490–495, 1969. · Zbl 0174.45402 · doi:10.1090/S0002-9904-1969-12213-5
[14] Fitzgibbon, W. E.,Semilinear Integrodifferential Equations in a Banach Space, Nonlinear Analysis: Theory, Methods and Applications, Vol. 4, pp. 745–760, 1980. · Zbl 0442.45014 · doi:10.1016/0362-546X(80)90075-9
[15] Heard, M. L.,An Abstract Semilinear Hyperbolic Volterra Integrodifferential Equation, Journal of Mathematical Analysis and Applications, Vol. 80, pp. 175–202, 1981. · Zbl 0468.45011 · doi:10.1016/0022-247X(81)90101-3
[16] Hussain, M. A.,On a Nonlinear Integrodifferential Equation in Banach Space, Indian Journal of Pure and Applied Mathematics, Vol. 19, pp. 516–529, 1988. · Zbl 0668.45011
[17] Miller, R. K.,Volterra Integral Equations in a Banach Space, Funkcialaj Ekvacioj, Vol. 18, pp. 163–193, 1975. · Zbl 0326.45007
[18] Pazy, A.,Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer Verlag, New York, New York, 1983. · Zbl 0516.47023
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.