A non-standard optimal control problem arising in an economic application

Alan, Zinober and Sufahani, Suliadi Firdaus (2013) A non-standard optimal control problem arising in an economic application. Presquisa Operacional, 33 (1). ISSN 1678-5142


Official URL: http://dx.doi.org/10.1590/S0101-74382013000100004


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) discrete-time results are also presented.

Item Type:Article
Uncontrolled Keywords:optimal control; non-standard optimal control; piecewise constant integrand; economics; comparative nonlinear programming results
Subjects:Q Science > QA Mathematics > QA63 Problem solving
Divisions:Faculty of Science, Technology and Human Development > Department of Science and Mathematics
ID Code:4320
Deposited By:Normajihan Abd. Rahman
Deposited On:15 Mar 2015 16:13
Last Modified:15 Mar 2015 16:13

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