A structured filter for Markovian switching systems

Abstract

In this work, a new methodology for the structuring of multiple model estimation schemas is developed. The proposed filter is applied to the estimation and detection of active mode in dynamic systems. The discrete-time Markovian switching systems represented by several linear models, associated with a particular operating mode, are studied. Therefore, the main idea of this work is the subdivision of the models set to some subsets in order to improve the detection and estimation performances. Each subset is associated with sub-estimators based on models of the subset. In order to compute the global estimate and subset probabilities, a global estimator is proposed. Theoretical developments based on a hierarchical decision, leading to more efficiency in detection and state estimation, are proposed. Naturally, these results can be used for fault detection and isolation, using the activation probabilities of operating modes. These results are applied to detect switches in the centre of gravity for vehicle roll dynamics. © 2014 Taylor & Francis

Novel Modeling and Filtering for Stochastic Switched Systems With Heterogeneous Behaviors

“…The potential individual switching characteristics of state evolution and measurement output motivate the framework for stochastic switched system with heterogeneous modes (1). Different from the conventional switched models where common switching signals are often shared (see, e.g., [16]- [20], [27]- [29]), our model allows for capturing the heterogeneity of state evolution and measurement output modes, which can accommodate the dynamical complexity and environmental changes in many real applications. Only scattered results are available on the stochastic switched systems with heterogeneous modes in the literatures.…”

“…Set the initial values x 0 = [2, −2] and P 0 = 0.1I. According to Theorem 5, the optimal linear filter of system ( 19) can be solved by means of the designed filter structure ( 12)- (16). Figures 1 and 2 respectively show the true state components and their estimates for α = 0.2, 0.5 and 0.9.…”

“…It is common to use Bernoulli binary switching sequences as an alternative approach to describe the network-induced uncertainties [14], [15]. Besides, switched systems, which consist of a finite number of subsystems and a switching mode signal that determines the active subsystem, have been extensively studied in many branches [16]- [20]. For other interesting schemes of stochastic switched systems, the references [21]- [26] may provide a boarder perspective.…”

Mixed and passive filtering for linear switched systems with average dwell time

“…As one typical example of constrained switching, the average dwell-time (ADT) logic was proposed in the work of Hespanha and Morse. [11][12][13] Among the various methods of state estimation, the H ∞ filtering keeps attracting more attention. [8][9][10] Along with the field of switched systems, the state estimation problem of dynamic systems has also received considerable attention because of its practical applications in signal processing and control.…”

“…[8][9][10] Along with the field of switched systems, the state estimation problem of dynamic systems has also received considerable attention because of its practical applications in signal processing and control. [11][12][13] Among the various methods of state estimation, the H ∞ filtering keeps attracting more attention. The advantage of H ∞ filtering is that there is no restriction on the statistical properties of disturbances, which is more general than the classical Kalman filtering.…”