belief functions for dynamical systems gipsalab ：动力系统实验室 gipsa信仰功能.pdf

Belief Functions for Dynamical Systems
1st spring school on belief functions theory and applications
Emmanuel Ramasso
Associate Professor at FEMTO-ST institute - Besan¸con
UMR CNRS 6174 - UFC / ENSMM / UTBM
Dep. Control Systems and Micro-Mechatronic Systems (AS2M)
-/~/
April 7th 2011
Topics
Dynamical systems
Consider a dynamical system (note: generally with constant parameters), Ex:
vehicle, human, machine. Provides a time-series (given sensors), generally
multi-dimensional.
Sensors are chosen to collect data (observations) concerning the system state.
States are considered imprecise and uncertain
Continuous states: Dynamics generally known, one wants to perform state
filtering/smoothing and sometimes classification. Use of filters like Kalman
(linear systems) or particle (non linear systems). Ex: positionning of targets.
Discrete states (with continuous or discrete observations): Dynamics are
generally estimated, one wants a segmentation of time-series and perform
sequence classification. Ex: human motion analysis, fault detection in
machines.
E. Ramasso (FEMTO-ST / AS2M) Belief Functions for Dynamical Systems April 7th 2011 2 / 73
Topics
Temporal Belief Functions
In this talk, system modelling is assumed to be made with belief functions
Continuous states: belief functions on reals (or intervals)
Discrete states: belief functions on discrete frame of discernement (FoD)
What are Temporal Belief Functions
Belief on states at t depends on some previous belief ( t − 1) and on
observations
Goals: makes belief or/and observations smooth, classify and/or segment
time-series
E. Ramasso (FEMTO-ST / AS2M) Belief Functions for Dynamical Sys