On the Existence and Design of Functional Observers for LTI Systems, with Application to User Modeling

Eskandari, Neda; Wang, Z. Jane; Dumont, Guy A.

doi:10.1002/asjc.1002

Cited by 8 publications

(3 citation statements)

References 44 publications

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“…These phenomena will influence the design process and performance of target tracking systems which is one of the important applications of wireless networks. The low observability inducted by complex data collection and communication schemes of wireless networks is a basic problem to be considered and solved for target state tracking estimation by wireless networks and more attention should be paid to it than the traditional state estimation and the ODA theory . The final purpose is to improve the estimator performance by using the result of the observable degree analysis.…”

Section: Introductionmentioning

confidence: 99%

Observable Degree Analysis to Match Estimation Performance for Wireless Tracking Networks

Chen

et al. 2016

Asian Journal of Control

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State estimation suffers some new challenging problems when wireless sensor networks (WSNs) are used in mobile target tracking systems. An important problem among them is low observability, which makes it necessary to further study performance of tracking estimators from an observable degree point of view. This paper studies observable degree analysis (ODA) to formulate the estimator performance for a kind of wireless tracking filter. For a kind of time-varying Kalman estimator, an improved ODA method is proposed by using weighted least square, Cauchy Schwarz inequality and normalization processing. The main contributions are that the relation is firstly analytically established between the observable degree and the estimation performance, and finally the observable degree is normalized in [0,1]. Meanwhile, observable degrees are both given for local state components and the global state. Thereby, we have the conclusion that higher observable degree corresponds to better estimation performance of the Kalman filter. Accordingly, it is potentially hopeful to achieve an effective function to study estimation performance of tracking estimators by directly using the observable degree. Simulation is provided to verify the results on real-time and generality, completeness and consistency/matching of the proposed observable degree analysis.

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Section: Introductionmentioning

confidence: 99%

Observable Degree Analysis to Match Estimation Performance for Wireless Tracking Networks

Chen

et al. 2016

Asian Journal of Control

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“…Under a special situation, when the functional distribution matrix is fixed at the identity matrix, the problem of ordinary full‐order observer is enclosed. Hence, FOs can have many applications in different areas of system monitoring, observer‐based control, and fault detection and identification of dynamic systems (see, e.g., ).…”

Section: Introductionmentioning

confidence: 99%

Minimum-order filter design for partial state estimation of linear systems with multiple time-varying state delays and unknown input delays

Mohajerpoor

Asayesh

Shanmugam

et al. 2016

Int. J. Robust. Nonlinear Control

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SUMMARYDesigning delay-dependent functional observers for LTI systems with multiple known time-varying state delays and unknown time-varying input delays is studied. The input delays are arbitrary, but the state delays should be upper-bounded. In addition, two scenarios of slow-varying and fast-varying state delays are investigated. The results of the paper can also be considered as one of the first contributions considering unknown-input functional observer design for linear systems with multiple time-varying state delays. Based on the Lyapunov Krasovskii approach, delay-dependent sufficient conditions of the exponential stability of the observer in each scenario are established in terms of linear matrix inequalities. Because of using effective techniques, such as the descriptor transformation and an advanced weighted integral inequality, the proposed stability criteria can result in larger stability regions compared with the other papers that study functional observers for time-varying delay systems. Furthermore, to help with the design procedure, a genetic algorithm-based scheme is proposed to adjust a weighting matrix in the established linear matrix inequalities. Two numerical examples illustrate the design procedure and demonstrate the efficacy of the proposed observer in each scenario.

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“…This approach can also be classified into three different schemes that are illustrated further in Section 2.1. The transformation‐based approaches have been applied to single and multi functional observers, as well as unknown‐input functional observers . It can be stated that most of the recent contributions in this field of research have used one of the schemes of this approach in their design procedures.…”

Section: Introductionmentioning

confidence: 99%

A New Algorithm to Design Minimal Multi‐Functional Observers for Linear Systems

Mohajerpoor¹,

Asayesh²,

Nahavandi³

2015

Asian Journal of Control

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Designing minimum possible order (minimal) observers for multi-input multi-output (MIMO) linear systems have always been an interesting subject. In this paper, a new methodology to design minimal multi-functional observers for linear time invariant (LTI) systems is proposed. The approach is applicable, and it also helps in regulating the convergence rate of the observed functions. It is assumed that the system is functional observable or functional detectable, which is less conservative than assuming the observability or detectability of the system. To satisfy the minimality of the observer, a recursive algorithm is provided that increases the order of the observer by appending the minimum required auxiliary functions to the desired functions that are going to be estimated. The algorithm increases the number of functions such that the necessary and sufficient conditions for the existence of a functional observer are satisfied. Moreover, a new methodology to solve the observer design interconnected equations is elaborated. Our new algorithm has advantages with regard to the other available methods in designing minimal order functional observers. Specifically, it is compared with the most common schemes, which are transformation based. Using numerical examples it is shown that under special circumstances, the conventional methods have some drawbacks. The problem partly lies in the lack of sufficient numerical degrees of freedom proposed by the conventional methods. It is shown that our proposed algorithm can resolve this issue. A recursive algorithm is also proposed to summarize the observer design procedure. Several numerical examples and simulation results illustrate the efficacy, superiority and different aspects of the theoretical findings.

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On the Existence and Design of Functional Observers for LTI Systems, with Application to User Modeling

Cited by 8 publications

References 44 publications

Observable Degree Analysis to Match Estimation Performance for Wireless Tracking Networks

Observable Degree Analysis to Match Estimation Performance for Wireless Tracking Networks

Minimum-order filter design for partial state estimation of linear systems with multiple time-varying state delays and unknown input delays

A New Algorithm to Design Minimal Multi‐Functional Observers for Linear Systems

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