Alan, Zinober and Sufahani, Suliadi Firdaus (2013) A nonstandard optimal control problem arising in an economic application. Presquisa Operacional, 33 (1). ISSN 16785142

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Abstract
A recent optimal control problem in the area of economics has mathematical properties that do not fall into the standard optimal control problem formulation. In our problem the state value at the final time the state, y(T) = z, is free and unknown, and additionally the Lagrangian integrand in the functional is a piecewise constant function of the unknown value y(T). This is not a standard optimal control problem and cannot be solved using Pontryagin's Minimum Principle with the standard boundary conditions at the final time. In the standard problem a free final state y(T) yields a necessary boundary condition p(T) = 0, where p(t) is the costate. Because the integrand is a function of y(T), the new necessary condition is that y(T) should be equal to a certain integral that is a continuous function of y(T). We introduce a continuous approximation of the piecewise constant integrand function by using a hyperbolic tangent approach and solve an example using a C++ shooting algorithm with Newton iteration for solving the Two Point Boundary Value Problem (TPBVP). The minimising free value y(T) is calculated in an outer loop iteration using the Golden Section or Brent algorithm. Comparative nonlinear programming (NP) discretetime results are also presented.
Item Type:  Article 

Uncontrolled Keywords:  optimal control; nonstandard optimal control; piecewise constant integrand; economics; comparative nonlinear programming results 
Subjects:  Q Science > QA Mathematics > QA63 Problem solving 
Divisions:  Faculty of Applied Science and Technology > Department of Science and Mathematics 
Depositing User:  Normajihan Abd. Rahman 
Date Deposited:  15 Mar 2015 08:13 
Last Modified:  15 Mar 2015 08:13 
URI:  http://eprints.uthm.edu.my/id/eprint/4320 
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