Constrained zonotopes: A new tool for set-based estimation and fault detection

Scott, Joseph K.; Raimondo, Davide M.; Marseglia, Giuseppe Roberto; Braatz, Richard D.

doi:10.1016/j.automatica.2016.02.036

Cited by 238 publications

(209 citation statements)

References 29 publications

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“…Though convex polytopes are closed for the operations of linear mapping and Minkowski sum, the complexity of both operations is exponential via H-rep in the worst case scenario [28]. By contrast, as shown in Tab.…”

Section: Set Operation Npmentioning

confidence: 99%

On enlarging backward reachable sets via Zonotopic set membership

Han

Rizaldi

El-Guindy

et al. 2016

2016 IEEE International Symposium on Intelligent Control (ISIC)

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Abstract-While a number of efficient methods have been proposed for approximating backward reachable sets, no synthesis method via backward reachable sets has been developed for estimating and enlarging the region of attraction (RA). This paper shows how to use backward reachable sets to enlarge the estimate of the RA of linear discrete-time systems, by using an optimal static feedback controller. Two controller design methods are provided: the first method enlarges the estimate of the RA via invariant sets, whose existence is ensured by zonotope containment; the second method provides the optimal control input by using Lyapunov stability and quadratic stabilization. The backward reachable set is represented by zonotopes which give a good compromise between accuracy and efficiency. The effectiveness of both methods is illustrated by a numerical example.

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Section: Set Operation Npmentioning

confidence: 99%

On enlarging backward reachable sets via Zonotopic set membership

Han

Rizaldi

El-Guindy

et al. 2016

2016 IEEE International Symposium on Intelligent Control (ISIC)

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“…However, the Minkowski sum and linear image (see Section 3) are outer-approximated. In the article [25], constrained zonotopes are introduced to overcome many of the limitations of zonotopes. These sets are closed under intersection, Minkowski sum, and linear image, and are capable of describing arbitrary convex polytopes if the complexity of the set description is not limited.…”

Section: Introductionmentioning

confidence: 99%

“…These sets are closed under intersection, Minkowski sum, and linear image, and are capable of describing arbitrary convex polytopes if the complexity of the set description is not limited. Efficient algorithms for linear set-valued state estimation and also FDI using constrained zonotopes are described in [25,8].…”

Section: Introductionmentioning

confidence: 99%

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Guaranteed methods based on constrained zonotopes for set-valued state estimation of nonlinear discrete-time systems

et al. 2020

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This paper presents new methods for set-valued state estimation of nonlinear discrete-time systems with unknown-but-bounded uncertainties. A single time step involves propagating an enclosure of the system states through the nonlinear dynamics (prediction), and then enclosing the intersection of this set with a bounded-error measurement (update). When these enclosures are represented by simple sets such as intervals, ellipsoids, parallelotopes, and zonotopes, certain set operations can be very conservative. Yet, using general convex polytopes is much more computationally demanding. To address this, this paper presents two new methods, a mean value extension and a first-order Taylor extension, for efficiently propagating constrained zonotopes through nonlinear mappings. These extend existing methods for zonotopes in a consistent way. Examples show that these extensions yield tighter prediction enclosures than zonotopic estimation methods, while largely retaining the computational benefits of zonotopes. Moreover, they enable tighter update enclosures because constrained zonotopes can represent intersections much more accurately than zonotopes. AbstractThis supplement details the derivation of the computational complexities of basic operations on zonotopes and constrained zonotopes, and the set-valued state estimators presented in the main paper.

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“…One alternative is to use the concept of zonotopes, described in [22] and further developed in [23], [24] and [25]. However, it is normally the case that each proposal represents a compromise between the computational complexity of the unions and intersections.…”

Section: Introductionmentioning

confidence: 99%

Fault detection for LPV systems using Set-Valued Observers: A coprime factorization approach

Silvestre

Rosa

Hespanha

et al. 2017

Systems & Control Letters

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This paper addresses the problem of fault detection for linear parameter-varying systems in the presence of measurement noise and exogenous disturbances using Set-Valued Observers (SVOs). The applicability of current methods is limited in the sense that, to increase accuracy, the detection requires a large number of past measurements and the boundedness of the set-valued estimates is only guaranteed for stable systems. In order to widen the class of systems to be modeled and also to reduce the associated computational cost, the aforementioned issues must be addressed. A solution involving left-coprime factorization and deadbeat observers is proposed that reduces the required number of past measurements without compromising accuracy and allowing the design of SVOs for fault detection of unstable systems by using the resulting coprime factorization stable subsystems. The algorithm is shown to produce bounded set-valued estimates and an example is provided. Performance is assessed through simulations, illustrating, in particular that small-magnitude faults (compared to exogenous disturbances) can be detected under mild assumptions.

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Constrained zonotopes: A new tool for set-based estimation and fault detection

Cited by 238 publications

References 29 publications

On enlarging backward reachable sets via Zonotopic set membership

On enlarging backward reachable sets via Zonotopic set membership

Guaranteed methods based on constrained zonotopes for set-valued state estimation of nonlinear discrete-time systems

Fault detection for LPV systems using Set-Valued Observers: A coprime factorization approach

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