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Optimal control problem via neural networks

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Abstract

This paper attempts to propose a new method based on capabilities of artificial neural networks, in function approximation, to attain the solution of optimal control problems. To do so, we try to approximate the solution of Hamiltonian conditions based on the Pontryagin minimum principle (PMP). For this purpose, we introduce an error function that contains all PMP conditions. In the proposed error function, we used trial solutions for the trajectory function, control function and the Lagrange multipliers. These trial solutions are constructed by using neurons. Then, we minimize the error function that contains just the weights of the trial solutions. Substituting the optimal values of the weights in the trial solutions, we obtain the optimal trajectory function, optimal control function and the optimal Lagrange multipliers.

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Authors and Affiliations

  1. Department of Applied Mathematics, Ferdowsi University of Mashhad, Mashhad, Iran

    Sohrab Effati & Morteza Pakdaman

  2. Center of Excellence on Soft Computing and Intelligent Information Processing, Ferdowsi University of Mashhad, Mashhad, Iran

    Sohrab Effati & Morteza Pakdaman

Authors
  1. Sohrab Effati
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  2. Morteza Pakdaman
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Correspondence to Morteza Pakdaman.

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Effati, S., Pakdaman, M. Optimal control problem via neural networks. Neural Comput & Applic 23, 2093–2100 (2013). https://doi.org/10.1007/s00521-012-1156-2

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  • DOI: https://doi.org/10.1007/s00521-012-1156-2

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