Journal of Applied Mathematics and Computing, Year (2007-5)

Title : ( SOLVING A SYSTEM OF THE NONLINEAR EQUATIONS BY ITERATIVE DYNAMIC PROGRAMMING )

Authors: Sohrab Effati ,

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Abstract. In this paper we use iterative dynamic programming in the discrete case to solve a wide range of the nonlinear equations systems. First, by defining an error function, we transform the problem to an optimal control problem in discrete case. In using iterative dynamic programming to solve optimal control problems up to now, we have broken up the problem into a number of stages and assumed that the performance index could always be expressed explicitly in terms of the state variables at the last stage. This provided a scheme where we could proceed backwards in a systematic way, carrying out optimization at each stage. Suppose that the performance index can not be expressed in terms of the variables at the last stage only. In other words, suppose the performance index is also a function of controls and variables at the other stages. Then we have a nonseparable optimal control problem. Furthermore, we obtain the path from the initial point up to the approximate solution.

Keywords

, Nonlinear equations system, optimal control, iterative dynamic programming
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@article{paperid:1009387,
author = {Effati, Sohrab},
title = {SOLVING A SYSTEM OF THE NONLINEAR EQUATIONS BY ITERATIVE DYNAMIC PROGRAMMING},
journal = {Journal of Applied Mathematics and Computing},
year = {2007},
month = {May},
issn = {1598-5865},
keywords = {Nonlinear equations system; optimal control; iterative dynamic programming (IDP).},
}

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%0 Journal Article
%T SOLVING A SYSTEM OF THE NONLINEAR EQUATIONS BY ITERATIVE DYNAMIC PROGRAMMING
%A Effati, Sohrab
%J Journal of Applied Mathematics and Computing
%@ 1598-5865
%D 2007

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