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Hybrid Functions Direct Approach and State Feedback Optimal Solutions for a Class of Nonlinear Polynomial Time Delay Systems

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  • Mohamed Karim Bouafoura
  • Naceur Benhadj Braiek

Abstract

The aim of this paper is to determine the optimal open loop solution and a nonlinear delay-dependent state feedback suboptimal control for a class of nonlinear polynomial time delay systems. The proposed method uses a hybrid of block pulse functions and Legendre polynomials as an orthogonal base for system’s states and input expansion. Hence, the complex dynamic optimization problem is then reduced, with the help of operational properties of the hybrid basis and Kronecker tensor product lemmas, to a nonlinear programming problem that could be solved with available NLP solvers. A practical nonlinear feedback controller gains are deduced with respect to a least square formalism based on the optimal open loop control results. Simulation results show efficiency of the proposed numerical optimal approach.

Suggested Citation

  • Mohamed Karim Bouafoura & Naceur Benhadj Braiek, 2019. "Hybrid Functions Direct Approach and State Feedback Optimal Solutions for a Class of Nonlinear Polynomial Time Delay Systems," Complexity, Hindawi, vol. 2019, pages 1-14, April.
    • Handle: RePEc:hin:complx:9596253
    DOI: 10.1155/2019/9596253
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    References listed on IDEAS

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    1. N. Haddadi & Y. Ordokhani & M. Razzaghi, 2012. "Optimal Control of Delay Systems by Using a Hybrid Functions Approximation," Journal of Optimization Theory and Applications, Springer, vol. 153(2), pages 338-356, May.
    2. F. Khellat, 2009. "Optimal Control of Linear Time-Delayed Systems by Linear Legendre Multiwavelets," Journal of Optimization Theory and Applications, Springer, vol. 143(1), pages 107-121, October.
    3. Changchun Hua & Shuangshuang Wu & Xian Yang & Xinping Guan, 2017. "Stability analysis of time-delay systems via free-matrix-based double integral inequality," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(2), pages 257-263, January.
    4. Changjun Yu & Qun Lin & Ryan Loxton & Kok Lay Teo & Guoqiang Wang, 2016. "A Hybrid Time-Scaling Transformation for Time-Delay Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 169(3), pages 876-901, June.
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