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Continuous approximation of 3 stepwise functions in the non-standard optimal control problem

W. Ahmad, Wan N. A. and Sufahani, Suliadi F. and Rusiman, Mohd Saifullah and Roslan, Rozaini and Khalid, Kamil and Che-Him, Norziha and Zinober, Alan (2017) Continuous approximation of 3 stepwise functions in the non-standard optimal control problem. Far East Journal of Mathematical Sciences (FJMS), 102 (11). pp. 2797-2807. ISSN 09720871

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A current ideal control issue in the region of financial aspects has numerical properties that do not fall into the standard optimal control problem detailing. In our concern, the state condition at the final time, y(T ) = z, is free and obscure, and furthermore, the integrand is a piecewise consistent capacity of the obscure esteem y(T ). This is not a standard optimal control problem and cannot be settled utilizing Pontryagin’s minimum principle with the standard limit conditions at the final time. In the standard issue, a free final state y(T ) yields an important limit condition p(T ) = 0, where p(t) is the costate. Since the integrand is a component of y(T ), the new fundamental condition is that y(T ) yield is equivalent to a specific necessary consistent capacity of z. We present a continuous approximation of the piecewise consistent integrand function through hyperbolic tangent approach and tackle a case utilizing a C++ shooting method. The limiting free y(T ) value is computed in an external circle emphasis through the golden section method.

Item Type: Article
Uncontrolled Keywords: Optimal control; calculus of variation; hyperbolic tangent
Subjects: Q Science > QA Mathematics > QA273 Probabilities. Mathematical statistics
Depositing User: Mr. Mohammad Shaifulrip Ithnin
Date Deposited: 30 Apr 2019 01:07
Last Modified: 30 Apr 2019 01:07
URI: http://eprints.uthm.edu.my/id/eprint/10986
Statistic Details: View Download Statistic

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