A NEW COMBINATION OF BROYDEN-FLETCHER-GOLDFARB-SHANNO AND BRENT TECHNIQUES IN SHOOTING METHOD FOR SOLVING NON-CLASSICAL OPTIMAL CONTROL PROBLEM

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 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 ) yields to be equivalent to a specific necessary that is a consistent capacity of z. We solve the two point boundary value problem (TPBVP) by combining the Broyden-Fletcher-Goldfarb-Shanno (BFGS) and Brent techniques in the shooting method. The limiting free y(T ) value is computed in an external circle emphasis through the Brent method. Comparative nonlinear programming through Euler and Runge-Kutta is also presented.