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Approximation procedures for the optimal control of bilinear and nonlinear systems

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Abstract

Optimal control problems for bilinear systems are studied and solved with a view to approximating analogous problems for general nonlinear systems. For a given bilinear optimal control problem, a sequence of linear problems is constructed, and their solutions are shown to converge to the desired solution. Also, the direct solution to the Hamilton-Jacobi equation is analyzed. A power-series approach is presented which requires offline calculations as in the linear case (Riccati equation). The methods are compared and illustrated. Relations to classical linear systems theory are discussed.

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Authors and Affiliations

  1. Instituto de Desarrollo Tecnológico para la Industria Química, CONICET-UNL, Santa Fe, Argentina

    W. A. Cebuhar (Research Fellow) & V. Costanza (Professor)

Authors
  1. W. A. Cebuhar
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  2. V. Costanza
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Communicated by G. Leitmann

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Cebuhar, W.A., Costanza, V. Approximation procedures for the optimal control of bilinear and nonlinear systems. J Optim Theory Appl 43, 615–627 (1984). https://doi.org/10.1007/BF00935009

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  • DOI: https://doi.org/10.1007/BF00935009

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