SOLVING A SYSTEM OF THE NONLINEAR EQUATIONS BY ITERATIVE DYNAMIC PROGRAMMING

Abstract

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