Guaranteed state estimation by zonotopes

Álamo, T.; Bravo, José Manuel; Camacho, Eduardo F.

doi:10.1109/cdc.2003.1271935

Cited by 195 publications

(430 citation statements)

References 12 publications

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“…In the work of Alamo et al (2005), a method computing a zonotope containing the intersection of a strip and a zonotope is given in Property A4. Based on this method, a zonotope containing x i,j,i k d can be constructed by considering (31) composed of q inequalities (i.e., strips).…”

Section: Fault Isolation Approachmentioning

confidence: 99%

Robust MPC for actuator-fault tolerance using set-based passive fault detection and active fault isolation

Puig

Ocampo‐Martínez

et al. 2014

53rd IEEE Conference on Decision and Control

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In this paper, a fault-tolerant control (FTC) scheme is proposed for actuator faults, which is built upon tube-based model predictive control (MPC) as well as set-based fault detection and isolation (FDI). In the class of MPC techniques, tubebased MPC can effectively deal with system constraints and uncertainties with relatively low computational complexity compared with other robust MPC techniques such as min-max MPC. Set-based FDI, generally considering the worst case of uncertainties, can robustly detect and isolate actuator faults. In the proposed FTC scheme, fault detection (FD) is passive by using invariant sets, while fault isolation (FI) is active by means of MPC and tubes. The active FI method proposed in this paper is implemented by making use of the constraint-handling ability of MPC to manipulate the bounds of inputs. After the system has been detected to become faulty, the input-constraint set of the MPC controller is adjusted to actively excite the system for achieving FI guarantees on-line, where an active FI-oriented input set is designed off-line. In this way, the system can be excited in order to obtain more extra system-operating information for FI than passive FI approaches. Overall, the objective of this paper is to propose an actuator MPC scheme with as little as possible of FI conservatism and computational complexity by combining tube-based MPC and set theory within the framework of MPC, respectively. Finally, a case study is used to show the effectiveness of the proposed FTC scheme.

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Section: Fault Isolation Approachmentioning

confidence: 99%

Robust MPC for actuator-fault tolerance using set-based passive fault detection and active fault isolation

Puig

Ocampo‐Martínez

et al. 2014

53rd IEEE Conference on Decision and Control

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“…In this case, the proposed set-membership approach and zonotopic Kalman observer in Section 3 and 4 can be applied to dynamical systems subject to unknown inputs, which can be considered an improvement on the methods presented in [1], [7]. Under this structure withT andN , the effects of unknown inputs can be decoupled.…”

Section: Extension To Dynamical Systems With Unknown Inputsmentioning

confidence: 99%

“…The zonotopic observer in combination with Kalman filtering is addressed in [6], [7]. Moreover, a set-membership approach based on zonotopes is proposed for dynamical systems in [1], [2].…”

Section: Introductionmentioning

confidence: 99%

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Set-membership approach and Kalman observer based on zonotopes for discrete-time descriptor systems

2018

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This paper proposes a set-membership state estimator and a zonotopic Kalman observer for discrete-time descriptor systems. Both approaches are developed in a set-based context considering system disturbances, measurement noise, and unknown inputs. This set-membership state estimation approach determines the set of consistent states with the model and measurements by constructing a parameterized intersection zonotope. Two methods to minimize the size of this intersection zonotope are provided: one inspired by Kalman filtering and the other based on solving an optimization problem involving a series of linear matrix inequalities. Additionally, we propose a zonotopic Kalman observer for discrete-time descriptor systems. Moreover, the relationship between both approaches is discussed. In particular, it is proved that the zonotopic Kalman observer in the current estimation type is equivalent to the set-membership approach. Finally, a numerical example is used to illustrate and compare the effectiveness of the proposed approaches.

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“…An alternative would be to use the concept of zonotopes, described in [7] and further developed in [11] and [1]. However, these represent a different compromise between the speed of the unions and intersections, with the intersections requiring more computations and introducing conservatism.…”

Section: Introductionmentioning

confidence: 99%

Self-Triggered and Event-Triggered Set-Valued Observers

Silvestre

Rosa

Hespanha

et al. 2018

Information Sciences

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This paper addresses the problem of reducing the required network load and computational power for the implementation of Set-Valued Observers (SVOs) in Networked Control System (NCS). Event-and self-triggered strategies for NCS, modeled as discrete-time Linear Parameter-Varying (LPV) systems, are studied by showing how the triggering condition can be selected. The methodology provided can be applied to determine when it is required to perform a full ("classical") computation of the SVOs, while providing low-complexity state overbounds for the remaining time, at the expenses of temporarily reducing the estimation accuracy. As part of the procedure, an algorithm is provided to compute a suitable centrally symmetric polytope that allows to find hyper-parallelepiped and ellipsoidal overbounds to the exact set-valued state estimates calculated by the SVOs. By construction, the proposed triggering techniques do not influence the convergence of the SVOs, as at some subsequent time instants, set-valued estimates are computed using the conventional SVOs. Results are provided for the triggering frequency of the self-triggered strategy and two interesting cases: distributed systems when the dynamics of all nodes are equal up to a reordering of the matrix; and when the probability distribution of the parameters influencing the dynamics is known. The performance of the proposed algorithm is demonstrated in simulation by using a time-sensitive example.

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Guaranteed state estimation by zonotopes

Cited by 195 publications

References 12 publications

Robust MPC for actuator-fault tolerance using set-based passive fault detection and active fault isolation

Robust MPC for actuator-fault tolerance using set-based passive fault detection and active fault isolation

Set-membership approach and Kalman observer based on zonotopes for discrete-time descriptor systems

Self-Triggered and Event-Triggered Set-Valued Observers

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