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On the convergence of successive Galerkin approximation for nonlinear output feedback H ∞ control

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Abstract

Although the formulation of the nonlinear theory of H ∞ control has been well developed, solving the Hamilton–Jacobi–Isaacs equation remains a challenge and is the major bottleneck for practical application of the theory. Several numerical methods have been proposed for its solution. In this paper, results on convergence and stability for a successive Galerkin approximation approach for nonlinear H ∞ control via output feedback are presented. An example is presented illustrating the application of the algorithm.

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Authors and Affiliations

  1. Department of Electrical Engineering, University of Brasília, Caixa Postal 04591, CEP 70910-900, Asa Norte, Brasília (DF), Brazil

    Henrique C. Ferreira

  2. Electro-Electronic Project Division, Brazilian Navy Technology Center, Av. Prof. Lineu Prestes, n. 2468, CEP 05508-000, São Paulo, SP, Brazil

    Paulo H. Rocha

  3. Department of Telecommunication and Control Engineering, University of São Paulo, Av. Prof. Luciano Gualberto, trav. 3, n. 158, CEP 05508-900, São Paulo, SP, Brazil

    Roberto M. Sales

Authors
  1. Henrique C. Ferreira
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  2. Paulo H. Rocha
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  3. Roberto M. Sales
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Correspondence to Henrique C. Ferreira.

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Ferreira, H.C., Rocha, P.H. & Sales, R.M. On the convergence of successive Galerkin approximation for nonlinear output feedback H ∞ control. Nonlinear Dyn 60, 651–660 (2010). https://doi.org/10.1007/s11071-009-9622-9

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  • DOI: https://doi.org/10.1007/s11071-009-9622-9

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