A comparative study for solving non-classical optimal control problem using euler, runge-kutta and shooting methods

Wan N. A. W. Ahmad

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Type :	article
Subject :	L Education (General)
ISSN :	0972-0871
Main Author :	Wan N. A. W. Ahmad
Additional Authors :	Mohd Saifullah Rusiman Suliadi Firdaus Sufahani Zinober, Alan Norazman Arbin
Title :	A comparative study for solving non-classical optimal control problem using euler, runge-kutta and shooting methods

Year of Publication :

2017

Abstract :

A current optimal control problem has the numerical properties that do not fall into the standard optimal control problem detailing. In our concern, the state incentive 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) yields to be equivalent to a necessary consistent capacity of z. We tackle a case utilizing a C++ shooting method with Newton emphasis for tackling the two point boundary value problem (TPBVP). The limiting free y(T) value is computed in an external circle emphasis through the golden section method. Comparative nonlinear programming through Euler and Runge-Kutta is also presented.

References

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