Comparison of guaranteed state estimators for linear time-invariant systems

Althoff, Matthias; Rath, Jagat Jyoti

doi:10.1016/j.automatica.2021.109662

Cited by 34 publications

(12 citation statements)

References 73 publications

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“…A recent study in [16] showed that the constrained zonotopic SMF proposed by [17] can give tighter estimates than other types of modern SMFs (e.g., ellipsoidal SMFs [9], [18] and zonotopic SMFs [12], [19]), which sheds new light on balancing the efficiency and the accuracy. This is largely because constrained zonotopes are closed under Minkowski sums and set intersections in the prediction and update steps, respectively.…”

Section: A Motivation and Related Workmentioning

confidence: 99%

Stability of Linear Set-Membership Filters

Cong¹,

Wang²,

Zhou³

2022

Preprint

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Stability is fundamental to filter design. It reflects the sensitivity of the estimate to initial conditions. In this paper, we focus on the stability of linear set-membership filters (SMFs), which has not yet been well understood. Considering linear time-invariant sampled-data systems, we explore the stability issue of the existing/classical SMFing framework and establish a new framework with guaranteed stability. First, we propose a new concept -the Observation-Information-Tower (OIT), which describes how the measurements affect the estimate in a setintersection manner. The OIT enables a rigorous stability analysis of the classical linear SMFing framework, where an explicit stability criterion is provided. It turns out that the classical framework requires the knowledge of the true initial range of the system state to guarantee stability, which is hence sensitive to initial conditions. To handle this problem, we establish an OITinspired filtering framework such that the stability is unaffected by the initial conditions. Under this stability-guaranteed framework, we develop a stable and fast constrained zonotopic SMF.

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Section: A Motivation and Related Workmentioning

confidence: 99%

Stability of Linear Set-Membership Filters

Cong¹,

Wang²,

Zhou³

2022

Preprint

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“…Gao et al 27 considered the control design under polytopic constraints and the optimal control input was obtained by solving a mixed integer linear algorithm. As shown in the work of Althoff and Rath, 28 zonotope has more accurate set representation than ellipsoid and less complexity than polytope. As a result, zonotopic set representation is considered in this article.…”

Section: Introductionmentioning

confidence: 98%

“…In summary, although there are some works [18][19][20][21][22][23][24][25][26] regarding CPS vulnerabilities based on reachability analysis have been reported in the literature, there is still room for improvement. As shown in the work of Althoff and Rath, 28 among various set representations, zonotope can achieve a good balance between accuracy and complexity. This motivates us to address CPS vulnerability using zonotopes.…”

Section: Introductionmentioning

confidence: 99%

A zonotopic characterization of cyber‐physical system vulnerabilities

Wang

Shen

et al. 2022

Intl J Robust & Nonlinear

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This article is concerned with the security of a cyber-physical system (CPS) against stealthy attacks. Stealthy attacks are malicious injections into sensor measurements without triggering detectors. We quantify the potential impact of stealthy attacks on system states using zonotopic reachable set. Then, a zonotopic framework is established to characterize the CPS vulnerabilities. Conditions for the existence of vulnerabilities are provided. Moreover, the level of such vulnerabilities is measured via one-sided Hausdorff distance. Finally, numerical simulations are conducted to demonstrate the effectiveness of the proposed method.

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“…Due to their fundamental property to enclose the solution to some mathematically formulated problem in a guaranteed way, they have many applications in engineering. These cover aspects such as state and parameter estimation [1], uncertainty quantification in robotics applications [21,24], or simulation of dynamic systems [23].…”

Section: Introductionmentioning

confidence: 99%

Verifying Provable Stability Domains for Discrete-Time Systems Using Ellipsoidal State Enclosures

2022

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Stability contractors, based on interval analysis, were introduced in recent work as a tool to verify stability domains for nonlinear dynamic systems. These contractors rely on the property that - in case of provable asymptotic stability - a certain domain in a multi-dimensional state space is mapped into its interior after a certain integration time for continuous-time processes or after a certain number of discretization steps in a discrete-time setting. However, a disadvantage of the use of axis-aligned interval boxes in such computations is the omnipresent wrapping effect. As shown in this contribution, the replacement of classical interval representations by ellipsoidal domain enclosures reduces this undesirable effect. It also helps to find suitable ratios for the edge lengths if interval-based domain representations are investigated. Moreover, ellipsoidal domains naturally represent the possible regions of attraction of asymptotically stable equilibrium points that can be analyzed with the help of quadratic Lyapunov functions, for which stability criteria can be cast into linear matrix inequality (LMI) constraints. For that reason, this paper further presents possible interfaces of ellipsoidal enclosure techniques with LMI approaches. This combination aims at the maximization of those domains that can be proven to be stable for a discrete-time range-only localization algorithm in robotics. There, an Extended Kalman Filter (EKF) is applied to a system for which the dynamics are characterized by a discrete-time integrator disturbance model with additive Gaussian noise. In this scenario, the measurement equations correspond to the distances between the object to be localized and beacons with known positions.

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Comparison of guaranteed state estimators for linear time-invariant systems

Cited by 34 publications

References 73 publications

Stability of Linear Set-Membership Filters

Stability of Linear Set-Membership Filters

A zonotopic characterization of cyber‐physical system vulnerabilities

Verifying Provable Stability Domains for Discrete-Time Systems Using Ellipsoidal State Enclosures

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