Variance-Constrained $H_{\infty }$ finite-horizon filtering for multi-rate time-varying networked systems based on stochastic protocols

Ming Lyu; Jie Zhang; YuMing Bo

Displaying similar documents to “Variance-Constrained $H_{\infty}$ finite-horizon filtering for multi-rate time-varying networked systems based on stochastic protocols”

Event-based multi-objective filtering for multi-rate time-varying systems with random sensor saturation

Hui Li, Ming Lyu, Baozhu Du (2020)

Kybernetika

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This paper focuses on the multi-objective filtering of multirate time-varying systems with random sensor saturations, where both the variance-constrained index and the $H_{\infty}$ index are employed to evaluate the filtering performance. According to address issues, the high-frequency period of the internal state of the system is nondestructively converted to the low-frequency period, which determined by the measurement devices. Then the saturated output of multiple sensors is modeled as a sector...

Distributed $H_{\infty}$ estimation for moving target under switching multi-agent network

Hu Chen, Qin Weiwei, He Bing, Liu Gang (2015)

Kybernetika

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In this paper, the distributed $H_{\infty}$ estimation problem is investigated for a moving target with local communication and switching topology. Based on the solution of the algebraic Riccati equation, a recursive algorithm is proposed using constant gain. The stability of the proposed algorithm is analysed by using the Lyapounov method, and a lower bound for estimation errors is obtained for the proposed common $H_{\infty}$ filter. Moreover, a bound for the $H_{\infty}$ parameter is obtained by means of the solution...

On risk reserve under distribution constraints

Mariusz Michta (2000)

Discussiones Mathematicae Probability and Statistics

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The purpose of this work is a study of the following insurance reserve model: $R (t) = η + \int_{0}^{t} p (s, R (s)) d s + \int_{0}^{t} σ (s, R (s)) d W_{s} - Z (t)$ , t ∈ [0,T], P(η ≥ c) ≥ 1-ϵ, ϵ ≥ 0. Under viability-type assumptions on a pair (p,σ) the estimation γ with the property: $i n f_{0 \leq t \leq T} P R (t) \geq c \geq γ$ is considered.

Stochastic convolution in separable Banach spaces and the stochastic linear Cauchy problem

Zdzisław Brzeźniak, Jan van Neerven (2000)

Studia Mathematica

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Let H be a separable real Hilbert space and let E be a separable real Banach space. We develop a general theory of stochastic convolution of ℒ(H,E)-valued functions with respect to a cylindrical Wiener process ${W_{t}^{H}}_{t \in [0, T]}$ with Cameron-Martin space H. This theory is applied to obtain necessary and sufficient conditions for the existence of a weak solution of the stochastic abstract Cauchy problem (ACP) $d X_{t} = A X_{t} d t + B d W_{t}^{H}$ (t∈ [0,T]), $X_{0} = 0$ almost surely, where A is the generator of a $C_{0}$ -semigroup ${S (t)}_{t \geq 0}$ of bounded linear...

Initial measures for the stochastic heat equation

Daniel Conus, Mathew Joseph, Davar Khoshnevisan, Shang-Yuan Shiu (2014)

Annales de l'I.H.P. Probabilités et statistiques

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We consider a family of nonlinear stochastic heat equations of the form $\partial_{t} u = ℒ u + σ (u) \dot{W}$ , where $\dot{W}$ denotes space–time white noise, $ℒ$ the generator of a symmetric Lévy process on $𝐑$ , and $σ$ is Lipschitz continuous and zero at 0. We show that this stochastic PDE has a random-field solution for every finite initial measure $u_{0}$ . Tight a priori bounds on the moments of the solution are also obtained. In the particular case that $ℒ f = c f^{''}$ for some $c g t; 0$ , we prove that if $u_{0}$ is a finite measure of compact support, then the...

Mobile robot localization under stochastic communication protocol

Yanyang Lu, Bo Shen (2020)

Kybernetika

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In this paper, the mobile robot localization problem is investigated under the stochastic communication protocol (SCP). In the mobile robot localization system, the measurement data including the distance and the azimuth are received by multiple sensors equipped on the robot. In order to relieve the network burden caused by network congestion, the SCP is introduced to schedule the transmission of the measurement data received by multiple sensors. The aim of this paper is to find a solution...

On pathwise uniqueness for stochastic differential equations driven by stable Lévy processes

Nicolas Fournier (2013)

Annales de l'I.H.P. Probabilités et statistiques

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We study a one-dimensional stochastic differential equation driven by a stable Lévy process of order $α$ with drift and diffusion coefficients $b$ , $σ$ . When $α \in (1, 2)$ , we investigate pathwise uniqueness for this equation. When $α \in (0, 1)$ , we study another stochastic differential equation, which is equivalent in law, but for which pathwise uniqueness holds under much weaker conditions. We obtain various results, depending on whether $α \in (0, 1)$ or $α \in (1, 2)$ and on whether the driving stable process is symmetric or not. Our...

Filter factors of truncated TLS regularization with multiple observations

Iveta Hnětynková, Martin Plešinger, Jana Žáková (2017)

Applications of Mathematics

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The total least squares (TLS) and truncated TLS (T-TLS) methods are widely known linear data fitting approaches, often used also in the context of very ill-conditioned, rank-deficient, or ill-posed problems. Regularization properties of T-TLS applied to linear approximation problems $A x \approx b$ were analyzed by Fierro, Golub, Hansen, and O’Leary (1997) through the so-called filter factors allowing to represent the solution in terms of a filtered pseudoinverse of $A$ applied to $b$ . This paper focuses...

$P_{λ}$ -sets and skeletal mappings

Aleksander Błaszczyk, Anna Brzeska (2013)

Colloquium Mathematicae

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We prove that if the topology on the set Seq of all finite sequences of natural numbers is determined by $P_{λ}$ -filters and λ ≤ , then Seq is a $P_{λ}$ -set in its Čech-Stone compactification. This improves some results of Simon and of Juhász and Szymański. As a corollary we obtain a generalization of a result of Burke concerning skeletal maps and we partially answer a question of his.

On reliability analysis of consecutive $k$ -out-of- $n$ systems with arbitrarily dependent components

Ebrahim Salehi (2016)

Applications of Mathematics

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In this paper, we consider the linear and circular consecutive $k$ -out-of- $n$ systems consisting of arbitrarily dependent components. Under the condition that at least $n - r + 1$ components ( $r \leq n$ ) of the system are working at time $t$ , we study the reliability properties of the residual lifetime of such systems. Also, we present some stochastic ordering properties of residual lifetime of consecutive $k$ -out-of- $n$ systems. In the following, we investigate the inactivity time of the component with lifetime...

Quasi-diffusion solution of a stochastic differential equation

Agnieszka Plucińska, Wojciech Szymański (2007)

Applicationes Mathematicae

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We consider the stochastic differential equation $X_{t} = X ₀ + \int_{0}^{t} (A_{s} + B_{s} X_{s}) d s + \int_{0}^{t} C_{s} d Y_{s}$ , where $A_{t}$ , $B_{t}$ , $C_{t}$ are nonrandom continuous functions of t, X₀ is an initial random variable, $Y = (Y_{t}, t \geq 0)$ is a Gaussian process and X₀, Y are independent. We give the form of the solution ( $X_{t}$ ) to (0.1) and then basing on the results of Plucińska [Teor. Veroyatnost. i Primenen. 25 (1980)] we prove that ( $X_{t}$ ) is a quasi-diffusion proces.

Systems of Bellman Equations to Stochastic Differential Games with Discount Control

Alain Bensoussan, Jens Frehse (2008)

Bollettino dell'Unione Matematica Italiana

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We consider two dimensional diagonal elliptic systems $\Delta u+au=H(x,u,\nabla u)$ which arise from stochastic differential games with discount control. The Hamiltonians $H$ have quadratic growth in $\nabla u$ and a special structure which has notyet been covered by regularity theory. Without smallness condition on $H$ , the existence of a regular solution is established.

Stochastic optimization problems with second order stochastic dominance constraints via Wasserstein metric

Vlasta Kaňková, Vadim Omelčenko (2018)

Kybernetika

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Optimization problems with stochastic dominance constraints are helpful to many real-life applications. We can recall e. g., problems of portfolio selection or problems connected with energy production. The above mentioned constraints are very suitable because they guarantee a solution fulfilling partial order between utility functions in a given subsystem $𝒰$ of the utility functions. Especially, considering $𝒰 : = 𝒰_{1}$ (where $𝒰_{1}$ is a system of non decreasing concave nonnegative utility functions)...

A continuous mapping theorem for the argmin-set functional with applications to convex stochastic processes

Dietmar Ferger (2021)

Kybernetika

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For lower-semicontinuous and convex stochastic processes $Z_{n}$ and nonnegative random variables $ϵ_{n}$ we investigate the pertaining random sets $A (Z_{n}, ϵ_{n})$ of all $ϵ_{n}$ -approximating minimizers of $Z_{n}$ . It is shown that, if the finite dimensional distributions of the $Z_{n}$ converge to some $Z$ and if the $ϵ_{n}$ converge in probability to some constant $c$ , then the $A (Z_{n}, ϵ_{n})$ converge in distribution to $A (Z, c)$ in the hyperspace of Vietoris. As a simple corollary we obtain an extension of several argmin-theorems in the literature. In particular,...

Displaying similar documents to “Variance-Constrained H ∞ finite-horizon filtering for multi-rate time-varying networked systems based on stochastic protocols”

Displaying similar documents to “Variance-Constrained $H_{\infty}$ finite-horizon filtering for multi-rate time-varying networked systems based on stochastic protocols”