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A Neural Network Approach for Solving a Class of Fractional Optimal Control Problems

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Abstract

In this paper the perceptron neural networks are applied to approximate the solution of fractional optimal control problems. The necessary (and also sufficient in most cases) optimality conditions are stated in a form of fractional two-point boundary value problem. Then this problem is converted to a Volterra integral equation. By using perceptron neural network’s ability in approximating a nonlinear function, first we propose approximating functions to estimate control, state and co-state functions which they satisfy the initial or boundary conditions. The approximating functions contain neural network with unknown weights. Using an optimization approach, the weights are adjusted such that the approximating functions satisfy the optimality conditions of fractional optimal control problem. Numerical results illustrate the advantages of the method.

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Authors and Affiliations

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

    Javad Sabouri K., 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. Javad Sabouri K.
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  2. Sohrab Effati
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  3. Morteza Pakdaman
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Correspondence to Sohrab Effati.

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Javad Sabouri K., Effati, S. & Pakdaman, M. A Neural Network Approach for Solving a Class of Fractional Optimal Control Problems. Neural Process Lett 45, 59–74 (2017). https://doi.org/10.1007/s11063-016-9510-5

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  • DOI: https://doi.org/10.1007/s11063-016-9510-5

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