A NON-STANDARD OPTIMAL CONTROL PROBLEM USING HYPERBOLIC TANGENT

Abstract

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 an 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 ) yield to be equivalent to a specific necessary that is a consistent capacity of z. We present a continuous estimation of the piecewise consistent integrand function through hyperbolic tangent approach and 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.