Zonotopes and Kalman observers: Gain optimality under distinct uncertainty paradigms and robust convergence

Combastel, Christophe

doi:10.1016/j.automatica.2015.03.008

Cited by 314 publications

(228 citation statements)

References 26 publications

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“…Based on the literature, interval dynamic systems are those uncertain systems whose uncertain parameters are bounded by intervals [Kolev and Petrakieva (2005) and Le et al (2012)]. Particularly, the wrapping effect appears in that kind of interval systems that are not monotonic [Puig et al (2005)].…”

Section: Dpi2014-58104-r) and By Agència De Gestió D'ajuts Universitamentioning

confidence: 99%

“…In set-based approaches, the set of states at time instant k + 1 is approximated by using propagation algorithms from the set of states at time k [Puig et al (2005), Combastel (2015)]. However, in set-based approaches, the parameter time invariance is not taken into account during the propagation of the uncertainties.…”

Section: Set-based Vs Trajectory-based Approachesmentioning

confidence: 99%

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Reduced-order Interval-observer Design for Dynamic Systems with Time-invariant Uncertainty

et al. 2017

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This paper addresses the design of reduced-order interval-observers for dynamic systems with time-invariant uncertainty. Because of the limitations of using the set-based approach to preserve the time dependency of parameter uncertainty and the wrapping effect to deal with interval-observers, the trajectory-based interval-observer approach is used with an appropriate observer gain. But, there could be some difficulties to satisfy the conditions for selecting a suitable gain to guarantee the positivity of the resulting observer. Then, a reducedorder observer is designed to reduce the computational complexity and to increase the degree of freedom when selecting the observer gain. Finally, a simulation example is employed for illustrating and analyzing the effectiveness of the proposed approach.

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Section: Dpi2014-58104-r) and By Agència De Gestió D'ajuts Universitamentioning

confidence: 99%

Section: Set-based Vs Trajectory-based Approachesmentioning

confidence: 99%

Reduced-order Interval-observer Design for Dynamic Systems with Time-invariant Uncertainty

et al. 2017

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“…A state bounding observer based on zonotopes is introduced in [5]. 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%

“…[1], [7], [12], [17], [18], [22] among others. In the literature, set-based state estimation approaches can be classified according to whether they follow a set-membership or an interval observer-based paradigm.…”

Section: Introductionmentioning

confidence: 99%

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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“…Most recently, Wang et al (2015a) proposed a novel fault estimation filter design method without constant fault assumption for discrete-time linear descriptor systems. On the other hand, Combastel (2015) presented a zonotopic Kalman observer which can provide interval estimation with optimal robust convergence. In this work, a novel zonotopic fault estimation method for discrete-time descriptor systems is developed by means of the interval observer-based approach within a set-theoretic framework.…”

Section: Introductionmentioning

confidence: 99%

Zonotopic Fault Estimation Filter Design for Discrete-time Descriptor Systems

Wang

Puig

et al. 2017

IFAC-PapersOnLine

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This paper considers actuator-fault estimation for discrete-time descriptor systems with unknown but bounded system disturbance and measurement noise. A zonotopic fault estimation filter is designed based on the analysis of fault detectability indexes. To ensure estimation accuracy, the filter gain in the zonotopic fault estimation filter is optimized through the zonotope minimization. The designed zonotopic filter not only can estimate fault magnitudes, but it also provides fault estimation results in an interval, i.e. the upper and lower bounds of fault magnitudes. Moreover, the proposed fault estimation filter has a non-singular structure and hence is easy to implement. Finally, simulation results are provided to illustrate the effectiveness of the proposed method.

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Zonotopes and Kalman observers: Gain optimality under distinct uncertainty paradigms and robust convergence

Cited by 314 publications

References 26 publications

Reduced-order Interval-observer Design for Dynamic Systems with Time-invariant Uncertainty

Reduced-order Interval-observer Design for Dynamic Systems with Time-invariant Uncertainty

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

Zonotopic Fault Estimation Filter Design for Discrete-time Descriptor Systems

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