Distributed filtering for time-varying systems over sensor networks with randomly switching topologies under the Round-Robin protocol

Bu, Xianye; Dong, Hongli; Han, Fei; Hou, Nan; Li, Gongfa

doi:10.1016/j.neucom.2018.07.087

Cited by 44 publications

(24 citation statements)

References 41 publications

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“…Real-world practitioners often prefer a combinational algorithm that incorporates first-order methods and second-order methods, such as Adam. In addition to the optimization methods, there is some effort dedicated to building the convex topological structures [42]. For example, Amos et al [43] developed a convex structure with a non-negative constraint on the hidden weight matrices.…”

Section: Information Transfer In Deep Neural Network: Training Netwomentioning

confidence: 99%

The expressivity and training of deep neural networks: Toward the edge of chaos?

Zhang

Li²,

Shen

et al. 2020

Neurocomputing

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Expressivity is one of the most significant issues in assessing neural networks. In this paper, we provide a quantitative analysis of the expressivity for the deep neural network (DNN) from its dynamic model, where the Hilbert space is employed to analyze the convergence and criticality. We study the feature mapping of several widely used activation functions obtained by Hermite polynomials, and find sharp declines or even saddle points in the feature space, which stagnate the information transfer in DNNs. We then present a new activation function design based on the Hermite polynomials for better utilization of spatial representation. Moreover, we analyze the information transfer of DNNs, emphasizing the convergence problem caused by the mismatch between input and topological structure. We also study the effects of input perturbations and regularization operators on critical expressivity. Our theoretical analysis reveals that DNNs use spatial domains for information representation and evolve to the edge of chaos as depth increases. In actual training, whether a particular network can ultimately arrive the edge of chaos depends on its ability to overcome convergence and pass information to the required network depth. Finally, we demonstrate the empirical performance of the proposed hypothesis via multivariate time series prediction and image classification examples.

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Section: Information Transfer In Deep Neural Network: Training Netwomentioning

confidence: 99%

The expressivity and training of deep neural networks: Toward the edge of chaos?

Zhang

Li²,

Shen

et al. 2020

Neurocomputing

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“…Then, the state estimator (7) and sensor guidance laws (27) with (29) can ensure that the error system (8) is exponentially stable in the sense of  1 -norm, and the  2 performance in (9) satisfies…”

Section: Theorem 1 Consider the Pde System (1)-(3) With The Measuredmentioning

confidence: 99%

“…Moreover, the sensor guidance laws (27) with (29) can improve the transient response of state estimation error.…”

Section: Theorem 1 Consider the Pde System (1)-(3) With The Measuredmentioning

confidence: 99%

“…L 0 e 2 x (0, x)dx; thus, (32) holds. Finally, from (36), we can get the exponential decay rate of the case for using mobile sensors is bigger than that of the static one, which implies that the guidance laws (27) with (29) can improve the state estimation error response speed, ie, the transient performance of the error system is enhanced. The proof is complete.…”

Section: Theorem 1 Consider the Pde System (1)-(3) With The Measuredmentioning

confidence: 99%

“…To overcome this difficulty, the distributed state estimation problem has attracted extensive concern in the past few years. [27][28][29][30] Compared with the centralized one, the distributed state estimator has its own advantages, such as low cost, low communication burden, and fast implementation. In the future work, we will deal with the distributed state estimator design for parabolic PDE systems with mobile sensor networks.…”

Section: Theorem 1 Consider the Pde System (1)-(3) With The Measuredmentioning

confidence: 99%

See 2 more Smart Citations

An enhanced state estimation for linear parabolic PDE systems with mobile sensors

Zhang

2019

Adaptive Control & Signal

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This paper studies an enhanced  2 state estimation problem of distributed parameter processes modeled by a linear parabolic partial differential equation using mobile sensors. The proposed estimation scheme contains a state estimator and the guidance of mobile sensors, where the spatial domain is decomposed into multiple subdomains according to the number of sensors and each sensor is capable of moving within the respective subdomain. The state estimator is desired to make the state estimation error system exponentially stable while providing an  2 performance bound. The mobile sensor guidance is used to enhance the transient performance of the error system. By the Lyapunov direct technique, an integrated design of state estimator and mobile sensor guidance laws is developed in the form of bilinear matrix inequalities (BMIs) to meet the desired design objectives. Moreover, to make the  2 performance bound as small as possible, a suboptimal enhanced  2 state estimation problem is formulated as a BMI optimization one, which can be solved via an iterative linear matrix inequality algorithm. Finally, numerical simulations are given to show the effectiveness of the proposed method.KEYWORDS distributed parameter processes, exponential stability, mobile sensor guidance, parabolic partial differential equation, state estimation 1552

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Distributed resilient state estimation for nonlinear systems with randomly occurring communication delays and missing measurements

Qian

Guo

Zhao

et al. 2021

Adaptive Control & Signal

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This article is concerned with the distributed H ∞ resilient state estimation problem for a class of nonlinear systems with randomly occurring communication delays and missing measurements in sensor networks. A novel sensor model is proposed, in which two Bernoulli distributed white sequences are introduced to describe the random communication delay and missing measurements in a unified framework. Meanwhile, the estimator gain is allowed to fluctuate within a certain range. Based on the developed model, a novel Lyapunov-Krasovskii functional with multiple delay information terms is constructed, then the stochastic analysis technique and the extended integral inequality are used to calculate the functional derivative. Consequently, the existence conditions for the required distributed estimator are established to ensure that the estimation error system is asymptotically mean-square stable and satisfies the prescribed H ∞ performance constraint, and the desired gain of distributed resilient estimator is also solved by linearizing the nonlinear terms. Finally, a numerical example is given to illustrate the effectiveness of the proposed algorithm.

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Distributed filtering for time-varying systems over sensor networks with randomly switching topologies under the Round-Robin protocol

Cited by 44 publications

References 41 publications

The expressivity and training of deep neural networks: Toward the edge of chaos?

The expressivity and training of deep neural networks: Toward the edge of chaos?

An enhanced state estimation for linear parabolic PDE systems with mobile sensors

Distributed resilient state estimation for nonlinear systems with randomly occurring communication delays and missing measurements

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