Algorithms for parameter optimization problems of nonlinear discrete systems

Abstract

This paper presents two algorithms for a class of optimization problems of the following form : min I (x) subject to the constraints

The constraints of this form come from the stability condition. The great difficulty of this problem is that there exists no method to check whether a point x is strictly in the feasible region.

In this work, for a class of function T (x, ω) we can define such a measure over the interval Ω that the corresponding "underestimated feasible region" should lie entirely in the feasible region.

Using this measure we can establish the algorithms which gives the asymptotical solution of the problem.

The convergence property of the algorithms and the estimation of the error of the solution are studied.