On environment mathematical model and on improved stable evolution in these hypotheses

Abstract

The subject of the paper is focused on the mathematical characterization of the environment through the mathematical model of the dynamic systems in general case when depend on parameters. A lot of results on the Liapunov stability of the dynamic system that depends on parameters, performed by us, are selected and explicitly accepted as properties that must describe the dynamic system of the environment. The property of separation between stable and unstable regions, in the domain of free parameters, on the matrix attached to the linear dynamic system mathematical model or to the “first approximation” of the nonlinear dynamic system was analysed. Our study is referred, as example, on particular case of biped walking robot model described by us in the paper that opened a way to perform the walking robot problems. Existence of the stable regions in the free parameters domain assures the possibility to realize stability control on each such region using a compatible criterion. A method for improved stable evolution of the environment’s dynamic system is proposed and analyzed on our case of biped walking robot where an important problem is selection of the parameters domain such that the dynamic system there exists and another important problem is optimization of stable evolution.