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

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• 作者：Javad Sabouri K. ; Sohrab Effati ; Morteza Pakdaman
• 关键词：Fractional optimal control problem ; Volterra integral equation ; Perceptron neural networks ; Unconstrained optimization
• 刊名：Neural Processing Letters
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：45
• 期：1
• 页码：59-74
• 全文大小：
• 刊物类别：Physics and Astronomy
• 刊物主题：Artificial Intelligence (incl. Robotics); Complex Systems; Computational Intelligence;
• 出版者：Springer US
• ISSN：1573-773X
• 卷排序：45

文摘

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.