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Related Experiment Video

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An efficient numerical scheme for solving fractional infinite-horizon optimal control problems.

Mina Yavari1, Alireza Nazemi1

  • 1Faculty of Mathematical Sciences, Shahrood University of Technology, Shahrood, Iran.

ISA Transactions
|June 11, 2019
PubMed
Summary

This study introduces a novel numerical method for fractional infinite-horizon optimal control problems using neural networks. The approach efficiently solves complex control systems involving Caputo fractional derivatives.

Keywords:
Caputo fractional derivativeChange of variableFractional infinite-horizon problemsNeural networksOptimal control problemOptimizationPontryagin minimum principle

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Area of Science:

  • Control Theory
  • Numerical Analysis
  • Computational Mathematics

Background:

  • Fractional calculus extends classical calculus, offering more sophisticated models for dynamic systems.
  • Infinite-horizon optimal control problems are crucial in various fields but computationally challenging, especially with fractional dynamics.

Purpose of the Study:

  • To develop an efficient numerical method for solving fractional infinite-horizon optimal control problems.
  • To transform these problems into a solvable finite-horizon form.
  • To utilize neural networks for approximating solutions.

Main Methods:

  • Transformation of the infinite-horizon problem to a finite-horizon one.
  • Approximation of Caputo fractional derivatives with integer-order derivatives.
  • Application of the Pontryagin minimum principle (PMP).
  • Construction of an unconstrained minimization problem using an error function.
  • Employing two-layered perceptron neural networks for state, costate, and control functions.

Main Results:

  • The proposed numerical method effectively handles fractional infinite-horizon optimal control problems.
  • The transformation and approximation techniques simplify the problem structure.
  • Neural network-based trial solutions provide accurate approximations for system states and controls.

Conclusions:

  • The presented method offers an efficient and accurate approach to solving a class of fractional optimal control problems.
  • This work contributes to the advancement of numerical techniques in fractional optimal control.
  • The use of neural networks demonstrates their potential in solving complex dynamic systems.