SciELO - Scientific Electronic Library Online

 
vol.33 número1Design to learn: customizing services when the future mattersUsing value-focused thinking in Brazil índice de autoresíndice de assuntospesquisa de artigos
Home Pagelista alfabética de periódicos  

Serviços Personalizados

Journal

Artigo

Indicadores

Links relacionados

Compartilhar


Pesquisa Operacional

versão impressa ISSN 0101-7438

Resumo

ZINOBER, Alan  e  SUFAHANI, Suliadi. A non-standard optimal control problem arising in an economics application. Pesqui. Oper. [online]. 2013, vol.33, n.1, pp.63-71. ISSN 0101-7438.  https://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.

Palavras-chave : optimal control; non-standard optimal control; piecewise constant integrand; economics; comparative nonlinear programming results.

        · texto em Inglês     · Inglês ( pdf )

 

Creative Commons License Todo o conteúdo deste periódico, exceto onde está identificado, está licenciado sob uma Licença Creative Commons