Set-valued estimation approach to recursive robust H∞ filtering

Ra, Won‐Sang; Jin, Seung Hee; Park, J.B.

doi:10.1049/ip-cta:20041051

Cited by 29 publications

(14 citation statements)

References 21 publications

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“…The topic of set-membership filtering has attracted a growing research interest, since it is based only on the knowledge of the hard bounds of the process and measurement noises [3,6,8,10,13,14,[16][17][18][19][20][21]29]. The idea of set-membership filtering is to provide all possible state estimates that are characterised by the set of state estimates consistent with both the observations received and the unknown but bounded process and measurement noises [3,10,20].…”

Section: Introductionmentioning

confidence: 99%

“…Hence the set-membership filtering problem aims to find the smallest characterisation of the feasible set of the states, rather than providing the most possible states under some optimality criteria, for example, Kalman filtering [2,27,33,34,36,38] and H 1 filtering [28,30,32]. Set-membership filtering is also called set-value filtering as the actual estimate is a set in state space rather than a single vector [14], [17], [21]. 0018-9251/09/$26.00 c°2009 IEEE Set-membership filtering problem was first considered by Witsenhausen [29].…”

Section: Introductionmentioning

confidence: 99%

“…For example, a combinational ellipsoidal bounded uncertain system was considered in [16]. The sum quadratic uncertain systems have been studied in [17]- [19]. For systems with both bounded noise and parametric uncertainty, a technique-based semi-definite optimization method has been proposed in [8] to handle several inequalities.…”

Section: Introductionmentioning

confidence: 99%

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Set-Membership Filtering with State Constraints

Yang

2009

IEEE Trans. Aerosp. Electron. Syst.

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In this paper, the problem of set-membership filtering is considered for discrete-time systems with equality and inequality constraints between their state variables. We formulate the problem of set-membership filtering as finding the set of estimates that belong to an ellipsoid. A centre and a shape matrix of the ellipsoid are used to describe the set of estimates and the solution to the set of estimates is obtained in terms of matrix inequality.Unknown but bounded process and measurement noises are handled under the inequality constraints by using S-procedure. I. INTRODUCTIONThe topic of set-membership filtering has attracted a growing research interest, since it is based only on the knowledge of the hard bounds of the process and measurement noises [3,6,8,10,13,14,[16][17][18][19][20][21]29]. The idea of set-membership filtering is to provide all possible state estimates that are characterised by the set of state estimates consistent with both the observations received and the unknown but bounded process and measurement noises [3,10,20]. The set-membership filtering can find a region in the state-space that guarantees to contain the unknown true state vector [13]. Hence the set-membership filtering problem aims to find the smallest characterisation of the feasible set of the states, rather than providing the most possible states under some optimality criteria, for example, Kalman filtering [2,27,33,34,36,38] Schweppe [20] for the set-membership filtering problem under the energy-type constraint. The solution to a set-membership filtering problem with the individual instantaneous constraints was determined by describing a bounding ellipsoid to the set of possible states [3]. The resulting filter is similar to that proposed by Schweppe [20], but it has an important advantage that the gain matrix does not depend on the particular output observations and is therefore precomputable. Recently, attempts have been made to deal with the set-membership filtering problems for uncertain systems. For example, a combinational ellipsoidal bounded uncertain system was considered in [16]. The sum quadratic uncertain systems have been studied in [17]-[19]. For systems with both bounded noise and parametric uncertainty, a technique-based semi-definite optimization method has been proposed in [8] to handle several inequalities. It has led to a simple and neat algorithm. We adopt this technique in this paper.However, in practical applications such as vehicle tracking, there are some hard constraints on the vehicle position when the vehicle is travelling on a known road (straight line or curve). Such tracking problem can be regarded as a filtering problem incorporating a state constraint with the road network information from digital maps [11,22,37]. This paper intends to study the set-membership filtering problem incorporating state constraints. The filtering problems with state constraints have been studied within the Kalman filter framework [9,24,31]. There have been several approaches to address this problem, which can be ...

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Set-Membership Filtering with State Constraints

Yang

2009

IEEE Trans. Aerosp. Electron. Syst.

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“…Ghaoui and Calafiore (2001), the convex optimization method has been employed to deal with the set-membership filtering for a class of norm bounded uncertainty system. In Ra, Jin, and Park (2004) and Savkin and Petersen (1995,9), a recursive method for constructing an ellipsoid state estimation set which is consistent with the measured output and the given noise has been proposed. The set-membership filtering problems have been investigated in Xia, Yang, and Han (2016) and Wei et al (2015) for a class of discrete time-varying systems with partial information transmission or with incomplete measurements.…”

Section: Set-membership Filtering For a Linear Systemmentioning

confidence: 99%

A survey on set-membership filtering for networked control systems under communication protocols

Dong

Han

et al. 2018

Systems Science & Control Engineering

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In recent years, the set-membership filtering problem has received extensive research interests due to its engineering significance to estimate a set which includes the true state of the system rather than a single vector. What's more, the communication protocol has been widely applied in the control systems because of its ability to prevent from data collisions and reduce the burden of the network. From the engineering practice, it is of vital importance to investigate the set-membership filtering under communication protocols. In this paper, a bibliographical review is provided on the set-membership filtering for networked control systems (NCSs) under communication protocols. Next, the concept of the NCS is briefly introduced. Some recent advances on the set-membership filtering problem for NCSs are summarized. Then, some well-known scheduling schemes are presented and the results of the set-membership filtering for NCSs under communication protocols are reviewed. Finally, some concluding remarks are given and some potential future research directions are pointed out. ARTICLE HISTORY

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“…Most publications on SMF deal with linear systems [7], [9], [13], [14], [18], [19], [22], [23], [25], [28]. Only a few consider nonlinear systems [20], [26], as it is not straightforward to use the EKF method where the nonlinear dynamics are linearized around a state estimate point by a first-order Taylor series approximation.…”

Section: Introductionmentioning

confidence: 99%

Set-Membership Fuzzy Filtering for Nonlinear Discrete-Time Systems

Yang

2010

IEEE Trans. Syst., Man, Cybern. B

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Abstract-This paper is concerned with the set-membership filtering (SMF) problem for discrete-time nonlinear systems. We employ the Takagi-Sugeno (T-S) fuzzy model to approximate the nonlinear systems over the true value of state and to overcome the difficulty with the linearization over a state estimate set rather than a state estimate point in the set-membership framework. Based on the T-S fuzzy model, we develop a new nonlinear SMF estimation method by using the fuzzy modeling approach and the S-procedure technique to determine a state estimation ellipsoid that is a set of states compatible with the measurements, the unknown-but-bounded process and measurement noises, and the modeling approximation errors. A recursive algorithm is derived for computing the ellipsoid that guarantees to contain the true state. A smallest possible estimate set is recursively computed by solving the semidefinite programming problem. An illustrative example shows the effectiveness of the proposed method for a class of discrete-time nonlinear systems via fuzzy switch.Index Terms-Convex optimization, linear set-membership filtering (SMF), nonlinear SMF, unknown-but-bounded noise, Takagi-Sugeno (T-S) fuzzy model.

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Set-valued estimation approach to recursive robust H∞ filtering

Cited by 29 publications

References 21 publications

Set-Membership Filtering with State Constraints

Set-Membership Filtering with State Constraints

A survey on set-membership filtering for networked control systems under communication protocols

Set-Membership Fuzzy Filtering for Nonlinear Discrete-Time Systems

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