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Approximate controllability for trajectories of semilinear control systems

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Abstract

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.

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References

  1. Naito, K.,Approximation and Controllability for Solutions of Semilinear Control Systems, Control Theory and Advanced Technology, Vol. 1, pp. 165–173, 1985.

    Google Scholar 

  2. Naito, K.,Controllability of Semilinear Control Systems, SIAM Journal on Control and Optimization, Vol. 25, pp. 715–722, 1987.

    Google Scholar 

  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.

    Google Scholar 

  5. Dauer, J. P.,A Controllability Technique for Nonlinear Systems,Journal of Mathematical Analysis and Applications, Vol. 37, pp. 442–451, 1972.

    Google Scholar 

  6. Hou, S. H.,Controllability and Feedback Systems, Nonlinear Analysis Theory, Methods, and Applications, Vol. 9, pp. 1487–1493, 1985.

    Google Scholar 

  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.

    Google Scholar 

  9. Pazy, A.,Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, New York, 1983.

    Google Scholar 

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Authors and Affiliations

  1. Department of Information Sciences, Tokyo Institute of Technology, Oh-Okayama Meguro-Ku, Tokyo, Japan

    K. Naito (Lecturer)

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  1. K. Naito
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Communicated by R. Conti

The author wishes to express his deep appreciation to Prof. T. I. Seidman for his many helpful suggestions and to Prof. W. Takahashi for many stimulating conversations.

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Naito, K. Approximate controllability for trajectories of semilinear control systems. J Optim Theory Appl 60, 57–65 (1989). https://doi.org/10.1007/BF00938799

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  • DOI: https://doi.org/10.1007/BF00938799

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