On the Practical Stabilization of Uncertain Systems: From Theory to Animation

Abstract

The Problem of ensuring the stability [l] of a controlled system under incomplete information on the inputs and system parameteres is one of the topics dealt with by the present theory of feedback control [2 - 4]. A conventional approach presumes here that the uncertain items involved are unknown but bounded. The mathematical tools required therefore lead to a natural formalisation in terms of the theory of trajectory tubes[5] incorporated through set-valued calculus and related techniques. However the practical direct use of these is difficult and computationally rather cumbersome. One of the schemes is to introduce set-valued approximations which are proposed here in the form of ellipsoidal - valued solutions implemented due to a comparison principle. The respective relations then allow effective algonthmizatxon and computer animation.