TY - GEN
T1 - Distribution-free mode-estimators for a class of discrete-time jump-linear systems
AU - Choukroun, Daniel
AU - Speyer, Jason L.
PY - 2005/12/1
Y1 - 2005/12/1
N2 - This paper is concerned with the development of recursive distribution-free mode-estimators for a class of discrete-time jump-linear systems. The cornerstone of the proposed filters consists of an algebraic manipulation of the dynamics equation of the continuous state. This equation turns out to be linear with respect to the mode vector, and, under the assumption of perfect state information, provides a linear observation equation for the mode. Appending this equation to the known linear dynamics equation of the mode yields a linear non-Gaussian state-space model. A first mode-estimator is then derived using standard Linear Filtering results. A second filter is developed as an application of a general discrete-time filter, which approximates the continuous-time optimal non-linear filter (the conditional mean estimator for continuous time) for small sample times. The second filter is preferred from a performance point of view. Model order reduction is applied in order to avoid singularity issues in the filters implementations. The second filter is envisioned as a useful tool in the analysis and design of dual controllers for this type of hybrid systems.
AB - This paper is concerned with the development of recursive distribution-free mode-estimators for a class of discrete-time jump-linear systems. The cornerstone of the proposed filters consists of an algebraic manipulation of the dynamics equation of the continuous state. This equation turns out to be linear with respect to the mode vector, and, under the assumption of perfect state information, provides a linear observation equation for the mode. Appending this equation to the known linear dynamics equation of the mode yields a linear non-Gaussian state-space model. A first mode-estimator is then derived using standard Linear Filtering results. A second filter is developed as an application of a general discrete-time filter, which approximates the continuous-time optimal non-linear filter (the conditional mean estimator for continuous time) for small sample times. The second filter is preferred from a performance point of view. Model order reduction is applied in order to avoid singularity issues in the filters implementations. The second filter is envisioned as a useful tool in the analysis and design of dual controllers for this type of hybrid systems.
KW - Finite-alphabet homogenous Markov chain
KW - Jump-linear system
KW - Optimal non-linear filtering
UR - http://www.scopus.com/inward/record.url?scp=33847192070&partnerID=8YFLogxK
U2 - 10.1109/CDC.2005.1583277
DO - 10.1109/CDC.2005.1583277
M3 - Conference contribution
AN - SCOPUS:33847192070
SN - 0780395689
SN - 9780780395688
T3 - Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
SP - 6928
EP - 6933
BT - Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
T2 - 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05
Y2 - 12 December 2005 through 15 December 2005
ER -