Set-valued solutions to impulsive differential inclusions

Abstract

This paper deals with the state estimation problem for impulsive control systems described by differential inclusions with measures. The problem is studied under uncertainty conditions with set-membership description of uncertain variables which are taken to be unknown but bounded with given bounds. Such problems arise from mathematical models of dynamical and physical systems for which we have an incomplete description of their generalized coordinates (e.g. the model may contain unpredictable errors without their statistical description). In this setting instead of an isolated trajectory of the dynamical control system we have a tube of such trajectories and the phase state vector should be replaced by the set of its possible values. The techniques of constructing the trajectory tubes and their cross-sections that may be considered as set-valued state estimates to differential inclusions with impulses are studied.

Keywords:

• Uncertainty
• control
• differential inclusions
• impulsive system

Acknowledgements

The research was supported by the Russian Foundation for Basic Research (RFBR) under project No. 03-01-00528, by the grant ‘Russian Scientific Schools’, No. 1889.2003.1, and by the Russian Academy of Sciences under project ‘The Program for Basic Researches, No. 19’.