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Hierarchic Control for the Wave Equation

Author

Listed:
  • Fágner Dias Araruna

    (Universidade Federal da Paraíba)

  • Enrique Fernández-Cara

    (Universidad de Sevilla)

  • Luciano Cipriano Silva

    (Universidade Federal da Paraíba)

Abstract

This paper deals with the hierarchical control of the wave equation. We use Stackelberg–Nash strategies. As usual, we consider one leader and two followers. To each leader we associate a Nash equilibrium corresponding to a bi-objective optimal control problem; then, we look for a leader that solves an exact controllability problem. We consider linear and semilinear equations.

Suggested Citation

  • Fágner Dias Araruna & Enrique Fernández-Cara & Luciano Cipriano Silva, 2018. "Hierarchic Control for the Wave Equation," Journal of Optimization Theory and Applications, Springer, vol. 178(1), pages 264-288, July.
    • Handle: RePEc:spr:joptap:v:178:y:2018:i:1:d:10.1007_s10957-018-1277-6
    DOI: 10.1007/s10957-018-1277-6
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    Cited by:

    1. Jiang, Jingfei & Guirao, Juan Luis García & Chen, Huatao & Cao, Dengqing, 2019. "The boundary control strategy for a fractional wave equation with external disturbances," Chaos, Solitons & Fractals, Elsevier, vol. 121(C), pages 92-97.
    2. Jiaquan Xie & Yongjiang Zheng & Zhongkai Ren & Tao Wang & Guangxian Shen, 2019. "Numerical Vibration Displacement Solutions of Fractional Drawing Self-Excited Vibration Model Based on Fractional Legendre Functions," Complexity, Hindawi, vol. 2019, pages 1-10, December.

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