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An alternative approach for non-linear optimal control problems based on the method of moments

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Abstract

We propose an alternative method for computing effectively the solution of non-linear, fixed-terminal-time, optimal control problems when they are given in Lagrange, Bolza or Mayer forms. This method works well when the nonlinearities in the control variable can be expressed as polynomials. The essential of this proposal is the transformation of a non-linear, non-convex optimal control problem into an equivalent optimal control problem with linear and convex structure. The method is based on global optimization of polynomials by the method of moments. With this method we can determine either the existence or lacking of minimizers. In addition, we can calculate generalized solutions when the original problem lacks of minimizers. We also present the numerical schemes to solve several examples arising in science and technology.

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Authors and Affiliations

  1. Departamento de Matemáticas, Universidad de los Andes, Carrera 1 No. 18A-70, Bogota, Colombia

    René Meziat & Diego Patiño

  2. E.T.S. de Ingenieros Industriales, Universidad de Castilla La Mancha, Edificio Politécnico, Ciudad Real, 13071, Spain

    Pablo Pedregal

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  1. René Meziat
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  2. Diego Patiño
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  3. Pablo Pedregal
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Correspondence to René Meziat.

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Meziat, R., Patiño, D. & Pedregal, P. An alternative approach for non-linear optimal control problems based on the method of moments. Comput Optim Appl 38, 147–171 (2007). https://doi.org/10.1007/s10589-007-9032-1

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