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 -