On the output controllability of a class of discrete nonlinear distributed systems: a fixed point theorem approach

  • Mustapha Lhous
  • Mostafa Rachik
  • Jamal Bouyaghroumni
  • Abdessamad Tridane
Article
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Abstract

Given a desired signal \( y^d= (y^{d}_{i})_{i \in \{0,\ldots ,N \}}\), we investigate the optimal control, which applied to nonlinear discrete distributed system \( x_{i+1} = Ax_i + Ex_{i} + Bu_i\), to give a desired output \( y^d \). Techniques based on the fixed point theorems for solving this problem are presented. An example and numerical simulation is also given.

Keywords

Output controllability Optimal control Nonlinear system Fixed point theorem 
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Notes

Acknowledgements

The authors would like to thank all the members of the Editorial Board who were responsible of this paper, and the anonymous referees for their valuable comments and suggestions to improve the content of this paper. This work is supported by the Morocco Systems Theory Network.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Mustapha Lhous
    • 1
  • Mostafa Rachik
    • 2
  • Jamal Bouyaghroumni
    • 2
  • Abdessamad Tridane
    • 3
  1. 1.Laboratory of Modeling, Analysis, Control and Statistics, Department of Mathematics and Computer Science, Faculty of Sciences Ain ChockHassan II University of CasablancaMaarif, CasablancaMorocco
  2. 2.Laboratory of Analysis Modelling and Simulation, Department of Mathematics and Computer Science, Faculty of Sciences Ben M’sikHassan II University of CasablancaSidi Othman, CasablancaMorocco
  3. 3.Department of Mathematical SciencesUnited Arab Emirates UniversityAl-AinUnited Arab Emirates

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