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**Boundary controllability of integrodifferential systems in Banach spaces.**
*(English)*
Zbl 0982.93017

Nonlinear, integrodifferential, nonstationary control systems defined in Banach spaces are considered. Using methods of functional analysis, sufficient conditions for exact boundary controllability in a given finite-time interval are formulated and proved. In the proofs of the main results, strongly continuous semigroup theory and the Banach fixed point contraction theorem are extensively used. Two examples which illustrate the theoretical considerations are also presented and discussed. Relationships to controllability results existing in the literature are given. Moreover, several remarks and comments concerning controllability problems for infinite-dimensional control systems are presented. Finally, it should be pointed out that similar controllability problems for nonlinear infinite-dimensional control systems have been recently considered in the paper [K. Balachandran, P. Balasubramaniam and J. P. Dauer, J. Optimization Theory Appl. 84, No. 1, 83-91 (1995; Zbl 0821.93010)].

Reviewer: J.Klamka (Katowice)

### MSC:

93B05 | Controllability |

93C25 | Control/observation systems in abstract spaces |

93C10 | Nonlinear systems in control theory |

### Keywords:

integrodifferential nonstationary control systems; Banach spaces; exact boundary controllability; semigroup theory; Banach fixed point contraction theorem; nonlinear infinite-dimensional control systems### Citations:

Zbl 0821.93010
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\textit{K. Balachandran} and \textit{E. R. Anandhi}, Proc. Indian Acad. Sci., Math. Sci. 111, No. 1, 127--135 (2001; Zbl 0982.93017)

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### References:

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[2] | Balachandran, K.; Dauer, J. P.; Balasubramaniam, P., Local null controllability of nonlinear functional differential systems in Banach spaces, J. Optim. Theory Appl., 88, 61-75 (1995) · Zbl 0848.93007 |

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[10] | Park, J. Y.; Han, H. K., Controllability of nonlinear functional integrodifferential systems in Banach space, Nihonkai Math. J., 8, 47-53 (1997) · Zbl 0997.93505 |

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