Compactness of the Set of Trajectories of the Control System Described by a Urysohn Type Integral Equation

Authors

  • Nesir Huseyin

DOI:

https://doi.org/10.11121/ijocta.01.2017.00299

Abstract

The control system with integralconstraint on the controls is studied, where the behavior of the system by a Urysohn type integral equation is described.  It is assumed thatthe system is nonlinear with respect to the state vector, affine with respect to the control vector.  The closed ball ofthe space $L_p(E;\mathbb{R}^m)$ $(p>1)$ with radius $r$ and centered at theorigin, is chosen as the set of admissible control functions, where $E\subset \mathbb{R}^k$ is a compact set. Itis proved that the set of trajectories generated by all admissible control functions is a compact subset of the space of continuous functions.

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Author Biography

Nesir Huseyin

Department of Elementary Mathematics Teching, Faculty of Education, Cumhuriyet University

Assistant Professor

 

References

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Crossref

Huseyin, A. and Huseyin, N., Precompactness of the set of trajectories of the controllable system described by a nonlinear Volterra integral equation, Math. Model. Anal., 17 (5), 686-695 (2012).

Crossref

Huseyin, N. and Huseyin, A., Compactness of the set of trajectories of the controllable system described by an affine integral equation, Appl. Math. Comput., 219 (16), 8416-8424 (2013).

Crossref

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Published

2016-12-12
CITATION
DOI: 10.11121/ijocta.01.2017.00299
Published: 2016-12-12

How to Cite

Huseyin, N. (2016). Compactness of the Set of Trajectories of the Control System Described by a Urysohn Type Integral Equation. An International Journal of Optimization and Control: Theories & Applications (IJOCTA), 7(1), 59–65. https://doi.org/10.11121/ijocta.01.2017.00299

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Research Articles