Title :
Conditional densities for continuous-time nonlinear hybrid systems with applications to fault detection
Author :
Hibey, Joseph L. ; Charalambous, Charalambos D.
Author_Institution :
Dept. of Electr. Eng., Colorado Univ., Denver, CO, USA
Abstract :
Continuous-time nonlinear stochastic differential state and measurement equations, all of which have coefficients capable of abrupt changes at a random time, are considered; finite-state jump Markov chains are used to model the changes. Conditional probability densities which are essential in obtaining filtered estimates for these hybrid systems are then derived. They are governed by a coupled system of stochastic partial differential equations. When the Q-matrix of the Markov chain is either lower or upper diagonal, it is shown that the system of conditional density equations is finite-dimensional computable. These findings are then applied to a fault detection problem to compute state estimates that include the failure time
Keywords :
Markov processes; continuous time systems; fault diagnosis; filtering theory; nonlinear dynamical systems; partial differential equations; probability; state estimation; Markov chain; Q-matrix; conditional probability densities; continuous-time nonlinear hybrid systems; failure time; fault detection; filtered estimates; finite-state jump Markov chains; stochastic partial differential equations; Density measurement; Electric variables measurement; Electrical fault detection; Fault detection; Filtering; Filters; Markov processes; Nonlinear equations; State-space methods; Stochastic systems;
Conference_Titel :
Decision and Control, 1998. Proceedings of the 37th IEEE Conference on
Conference_Location :
Tampa, FL
Print_ISBN :
0-7803-4394-8
DOI :
10.1109/CDC.1998.760849