Synchronization in Networks of Identical Nonlinear Systems via Dynamic Dead Zones

Casadei, Giacomo; Astolfi, Daniele; Alessandri, A.; Zaccarian, Luca

doi:10.1109/lcsys.2019.2916249

Cited by 21 publications

(18 citation statements)

References 30 publications

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“…Figures 1 and 2 showcase the transient behavior of the state variables and corresponding estimates in two different simulation runs, i.e., in a noise-free case and under the presence of random noises. Such simulation runs show that the time response of the observer is less than the oscillation period of the oscillators, namely it converges quite quickly in such a way as to feed the possible close-loop controllers with the estimates for the purpose of syncronization (see [47] and the references therein). The behaviors at the regime can be analyzed by looking at Figures 3 and 4.…”

Section: Numerical Resultsmentioning

confidence: 99%

Lyapunov Functions for State Observers of Dynamic Systems Using Hamilton–Jacobi Inequalities

Alessandri

2020

Mathematics

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Lyapunov functions enable analyzing the stability of dynamic systems described by ordinary differential equations without finding the solution of such equations. For nonlinear systems, devising a Lyapunov function is not an easy task to solve in general. In this paper, we present an approach to the construction of Lyapunov funtions to prove stability in estimation problems. To this end, we motivate the adoption of input-to-state stability (ISS) to deal with the estimation error involved by state observers in performing state estimation for nonlinear continuous-time systems. Such stability properties are ensured by means of ISS Lyapunov functions that satisfy Hamilton–Jacobi inequalities. Based on this general framework, we focus on observers for polynomial nonlinear systems and the sum-of-squares paradigm to find such Lyapunov functions.

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Section: Numerical Resultsmentioning

confidence: 99%

Lyapunov Functions for State Observers of Dynamic Systems Using Hamilton–Jacobi Inequalities

Alessandri

2020

Mathematics

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“…Fortunately, the developed result can be easily extended to this case via replacing

Γ_{1, \hat{x}, k}^{i} = - ξ^{i} \sum_{j \in M_{i}} l_{i j} ({\hat{x}}_{p_{j, r}}^{j} - {\hat{x}}_{p_{j, r}}^{i})

Γ_{1, \hat{x}, k}^{i, ρ} = - ξ^{i} \sum_{j \in M_{i}} l_{i j} ρ^{i} ({\hat{x}}_{p_{j, r}}^{j} - {\hat{x}}_{p_{j, r}}^{i})

in Theorem 1. On the other hand, different from the dependence of the whole Laplacian matrix in the literatures, 44,45 the desired parameter

K_{k}^{i}

in our article is implicitly related with the local communication topology, that is, the i th row of the Laplacian matrix. In other words, the Laplacian matrix combined with the received neighboring estimates (i.e., the term

Γ_{1, \hat{x}, k}^{i}

) definitely affects the volume of the estimated ellipsoid

({\hat{x}}_{k + 1}^{i}, P_{k + 1}^{i})

.…”

Section: Design Of Distributed Stubborn‐set‐membership Filtersmentioning

confidence: 99%

“…In addition, it should be pointed out that the conception of artificial stubborn constraint comes from that in the literatures. 40,44,45 Especially, a novel approach of dynamic saturation redesign with an adaptive rule has been developed in the literatures 44,45 to realize the synchronization of complex dynamical systems while mitigating the impact of impulsive perturbations. In these two articles, the developed results clearly disclose the influence from the connection topology benefiting from the utilization of the approaches of steady-state performance analysis and therefore it is of crucial importance to investigate the distributed filtering issues under the worst case with a common parameter K and shape matrix P.…”

Section: Parameter Optimizationmentioning

confidence: 99%

“…By contrast to the literatures, 22,31 the main differences are shown in the following three aspects: (i) the constructed filter includes a consensus term to reduce the potential disagreement, (ii) different from the dependency on gaps, the dynamical rule on the event‐triggering threshold is driven by an input with exponential decay, and (iii) a stubborn constraint

ρ^{i} (y_{k}^{i} - C_{k}^{i} {\hat{x}}_{k}^{i})

is employed to remove the abnormal measurements. In addition, it should be pointed out that the conception of artificial stubborn constraint comes from that in the literatures 40,44,45 . Especially, a novel approach of dynamic saturation redesign with an adaptive rule has been developed in the literatures 44,45 to realize the synchronization of complex dynamical systems while mitigating the impact of impulsive perturbations.…”

Section: Design Of Distributed Stubborn‐set‐membership Filtersmentioning

confidence: 99%

See 1 more Smart Citation

Distributed stubborn‐set‐membership filtering with a dynamic event‐based scheme: The Takagi‐Sugeno fuzzy framework

Mao

Ding

Wei

2020

Adaptive Control & Signal

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The article develops a novel stubborn set-membership filtering with the dynamic event-triggered scheme for discrete-time nonlinear systems with the state-delays, unknown-but-bounded noises as well as abnormal measurements.First, in comparison with traditional event schemes, a dynamic event-triggered scheme with a time-varying auxiliary offset variable in the threshold is employed to schedule the access token with the purpose of mitigating the communication burden. A novel fuzzy stubborn filter in a distributed way is then constructed to obtain the ellipsoid set including the real state while constraining the direct influence of abnormal measurements, which could come from outliers or a malicious modification by attackers. An algorithm with the form of recursive linear matrix inequalities is presented to determine the desired ellipsoids as well as the distributed filter gains, where the operation of the algorithm do not depend on the global information of network topology. Finally, the validity of the proposed scheme is illustrated via an inverted pendulum system.

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“…Then, we propose two different methodologies to redesign the output injection term, both of them preserving ISS. The first one, called stubborn redesign, was first introduced in the context of linear systems [5], [6], and high-gain observers [9], and aftewards used in Kalman filters [26], neural networks [35] and synchronization [21], [22]. It consists in adding an adaptive saturation to the output injection error in the observer dynamics so as to reduce the sensitivity to measurement outliers.…”

Section: Introductionmentioning

confidence: 99%

Stubborn and Dead-Zone Redesign for Nonlinear Observers and Filters

Astolfi

Alessandri

Zaccarian

2021

IEEE Trans. Automat. Contr.

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We propose a redesign paradigm for stable estimators by introducing a saturation or a dead-zone nonlinearity with adaptive thresholds on the output injection term. Such nonlinearities allow improving the sensitivity to measurement noise in different scenarios (impulsive disturbances or persistent noise such as sensor bias), while preserving the asymptotic convergence properties of the original observer. These redesigns apply to a broad class of state estimators, including linear observers, observers for input-affine systems, observers for Lipschitz systems, observers based on the circle criterion, high-gain observers, standard and extended Kalman filters. Simulation results confirm the effectiveness of both the stubborn and dead-zone redesigns.

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Synchronization in Networks of Identical Nonlinear Systems via Dynamic Dead Zones

Cited by 21 publications

References 30 publications

Lyapunov Functions for State Observers of Dynamic Systems Using Hamilton–Jacobi Inequalities

Lyapunov Functions for State Observers of Dynamic Systems Using Hamilton–Jacobi Inequalities

Distributed stubborn‐set‐membership filtering with a dynamic event‐based scheme: The Takagi‐Sugeno fuzzy framework

Stubborn and Dead-Zone Redesign for Nonlinear Observers and Filters

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