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Approximate controllability for trajectories of semilinear control systems. (English) Zbl 0632.93007
We treat an abstract semilinear control system and study the controllability problem for its trajectories. Assuming a range condition of the control action operator and an inequality condition on the system parameters, we can show that the reachable trajectory set of the semilinear system is equivalent to that of its corresponding linear system.
Reviewer: K.Naito

MSC:
93B05Controllability
93C10Nonlinear control systems
93C25Control systems in abstract spaces
93B03Attainable sets
References:
[1]Naito, K.,Approximation and Controllability for Solutions of Semilinear Control Systems, Control Theory and Advanced Technology, Vol. 1, pp. 165-173, 1985.
[2]Naito, K.,Controllability of Semilinear Control Systems, SIAM Journal on Control and Optimization, Vol. 25, pp. 715-722, 1987. · Zbl 0617.93004 · doi:10.1137/0325040
[3]Naito, K.,An Inequality Condition for Approximate Controllability of Semilinear Control Systems, Journal of Mathematical Analysis and Applications (to appear).
[4]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.
[5]Dauer, J. P.,A Controllability Technique for Nonlinear Systems,Journal of Mathematical Analysis and Applications, Vol. 37, pp. 442-451, 1972. · Zbl 0224.93006 · doi:10.1016/0022-247X(72)90286-7
[6]Hou, S. H.,Controllability and Feedback Systems, Nonlinear Analysis Theory, Methods, and Applications, Vol. 9, pp. 1487-1493, 1985. · Zbl 0621.93007 · doi:10.1016/0362-546X(85)90101-4
[7]Seidman, T. I.,Invariance under nonlinear Perturbations for Reachable and Almost-Reachable Sets, Proceedings of the IFIP Symposium on Control Theory for Partial Differential Equations, Gainesville, Florida, 1986, Edited by I. Lasiecka, Springer-Verlag, New York, New York (to appear).
[8]Seidman, T. I.,Invariance on the Reachable Sets under Nonlinear Perturbations, SIAM Journal on Control and Optimization, Vol. 25, pp. 1173-1191, 1987. · Zbl 0626.49018 · doi:10.1137/0325064
[9]Pazy, A.,Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, New York, 1983.