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Approximate Controllability of Second-Order Semilinear Control System

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Abstract

This paper deals with the approximate controllability of second-order semilinear control system in Hilbert spaces under the assumption that the corresponding linear system is approximately controllable. The control function for this system is suitably constructed, and the sufficient conditions for the approximate controllability of the proposed problem in Hilbert spaces are established. The results are obtained when the nonlinearity satisfying the monotone condition and integral contractor condition. Finally, an example is provided to illustrate the application of the obtained results.

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Acknowledgments

The first author would like to thank Council of Scientific and Industrial Research, New Delhi, Government of India (Grant No. 9924-11-44), for financial support and to carry out his research work.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, 247667, Uttarakhand, India

    Anurag Shukla, N. Sukavanam, D. N. Pandey & Urvashi Arora

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  1. Anurag Shukla
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  2. N. Sukavanam
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  3. D. N. Pandey
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  4. Urvashi Arora
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Correspondence to Anurag Shukla.

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Shukla, A., Sukavanam, N., Pandey, D.N. et al. Approximate Controllability of Second-Order Semilinear Control System. Circuits Syst Signal Process 35, 3339–3354 (2016). https://doi.org/10.1007/s00034-015-0191-5

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  • DOI: https://doi.org/10.1007/s00034-015-0191-5

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