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Showing papers on "Stochastic process published in 2020"


Journal ArticleDOI
TL;DR: In this paper, the authors consider stochastic processes under resetting, which have attracted a lot of attention in recent years, and discuss multiparticle systems as well as extended systems, such as fluctuating interfaces.
Abstract: In this Topical Review we consider stochastic processes under resetting, which have attracted a lot of attention in recent years. We begin with the simple example of a diffusive particle whose position is reset randomly in time with a constant rate r, which corresponds to Poissonian resetting, to some fixed point (e.g. its initial position). This simple system already exhibits the main features of interest induced by resetting: (i) the system reaches a nontrivial nonequilibrium stationary state (ii) the mean time for the particle to reach a target is finite and has a minimum, optimal, value as a function of the resetting rate r. We then generalise to an arbitrary stochastic process (e.g. Levy flights or fractional Brownian motion) and non-Poissonian resetting (e.g. power-law waiting time distribution for intervals between resetting events). We go on to discuss multiparticle systems as well as extended systems, such as fluctuating interfaces, under resetting. We also consider resetting with memory which implies resetting the process to some randomly selected previous time. Finally we give an overview of recent developments and applications in the field. PACS numbers: 05.40.-a, 05.70.Fh, 02.50.Ey, 64.60.-i arXiv:1910.07993v2 [cond-mat.stat-mech]

361 citations


Journal ArticleDOI
TL;DR: This article tackles the recursive filtering problem for a class of stochastic nonlinear time-varying complex networks suffering from both the state saturations and the deception attacks, and designs a state-saturated recursive filter such that a certain upper bound is guaranteed on the filtering error covariance and is then minimized at each time instant.
Abstract: This article tackles the recursive filtering problem for a class of stochastic nonlinear time-varying complex networks (CNs) suffering from both the state saturations and the deception attacks. The nonlinear inner coupling and the state saturations are taken into account to characterize the nonlinear nature of CNs. From the defender’s perspective, the randomly occurring deception attack is governed by a set of Bernoulli binary distributed white sequence with a given probability. The objective of the addressed problem is to design a state-saturated recursive filter such that, in the simultaneous presence of the state saturations and the randomly occurring deception attacks, a certain upper bound is guaranteed on the filtering error covariance, and such an upper bound is then minimized at each time instant. By employing the induction method, an upper bound on the filtering error variance is first constructed in terms of the solutions to a set of matrix difference equations. Subsequently, the filter parameters are appropriately designed to minimize such an upper bound. Finally, a numerical simulation example is provided to demonstrate the feasibility and usefulness of the proposed filtering scheme.

164 citations


Journal ArticleDOI
TL;DR: The problem of input-to-state stability (ISS) is systematically investigated for nonlinear systems with stochastic impulses and an example of coordination of multi-agent systems is provided to illustrate the effectiveness of the proposed new stability criteria.

123 citations


Journal ArticleDOI
TL;DR: Markov categories are developed as a framework for synthetic probability and statistics, following work of Golubtsov as well as Cho and Jacobs, and provides a uniform treatment of various types of probability theory.

117 citations


Journal ArticleDOI
TL;DR: A novel memory interconnection Lyapunov–Krasovskii functional is structured by taking full advantage of more information of sampling interval and state, and developing some new terms to investigate the finite-time (FT) H∞ synchronization issue for complex networks with stochastic cyber attacks and random memory information exchanges.

106 citations


Journal ArticleDOI
09 Aug 2020
TL;DR: This article aims to provide a comprehensive review of classical random walks and quantum walks, including basic concepts and some typical algorithms, and introduces their applications in the field of computer science.
Abstract: A random walk is known as a random process which describes a path including a succession of random steps in the mathematical space. It has increasingly been popular in various disciplines such as mathematics and computer science. Furthermore, in quantum mechanics, quantum walks can be regarded as quantum analogues of classical random walks. Classical random walks and quantum walks can be used to calculate the proximity between nodes and extract the topology in the network. Various random walk related models can be applied in different fields, which is of great significance to downstream tasks such as link prediction, recommendation, computer vision, semi-supervised learning, and network embedding. In this article, we aim to provide a comprehensive review of classical random walks and quantum walks. We first review the knowledge of classical random walks and quantum walks, including basic concepts and some typical algorithms. We also compare the algorithms based on quantum walks and classical random walks from the perspective of time complexity. Then we introduce their applications in the field of computer science. Finally we discuss the open issues from the perspectives of efficiency, main-memory volume, and computing time of existing algorithms. This study aims to contribute to this growing area of research by exploring random walks and quantum walks together.

92 citations


Journal ArticleDOI
TL;DR: It is shown that a similar accuracy as with a FE 2 multi-scale simulation can be reached with the RNN-based surrogate model as long as the local strain state remains in the training range, while the computational time is reduced by four orders of magnitude.

90 citations


Journal ArticleDOI
TL;DR: The uniform-in-time strong convergence for second order systems under suitable contraction conditions is shown and the application of RBM for singular interaction kernels via kernel splitting strategy is proposed and numerically the application to molecular dynamics is investigated.

89 citations


Journal ArticleDOI
Xiao-Meng Li1, Bin Zhang1, Panshuo Li1, Qi Zhou1, Renquan Lu1 
TL;DR: The problem of finite-horizon state estimator design for periodic neural networks over multiple fading channels is studied and two sufficient criteria are provided, by utilizing a stochastic analysis approach, to guarantee that the estimation error system is stochastically stable.
Abstract: The problem of finite-horizon $H_{\infty}$ state estimator design for periodic neural networks over multiple fading channels is studied in this paper. To characterize the measurement signals transmitted through different channels experiencing channel fading, a multiple fading channels model is considered. For investigating the situation of correlated fading channels, a set of correlated random variables is introduced. Specifically, the channel coefficients are described by white noise processes and are assumed to be correlated. Two sufficient criteria are provided, by utilizing a stochastic analysis approach, to guarantee that the estimation error system is stochastically stable and achieves the prescribed $H_{\infty}$ performance. Then, the parameters of the estimator are derived by solving recursive linear matrix inequalities. Finally, some simulation results are shown to illustrate the effectiveness of the proposed method.

89 citations


Journal ArticleDOI
TL;DR: The aim of this paper is to design a dynamic output feedback controller that achieves the described security in probability, and some novel sufficient conditions are proposed to guarantee the input-to-state stability of the system in probability.
Abstract: This paper is concerned with the event-based security control problems for a set of discrete-time stochastic systems suffered from randomly occurred attacks, especially the denial-of-service attacks and the deception attacks. An attack model with compensation is established to describe combinations of attacks to the networked control systems. An event-triggered mechanism is employed to debase the communication load by transmitting measurement signals when a definite triggering condition is satisfied. A definition of security probability is proposed to describe the transient state of controller systems. The aim of this paper is to design a dynamic output feedback controller, thereupon the closed-loop system achieves the described security in probability. Some novel sufficient conditions are proposed to guarantee the input-to-state stability of the system in probability, and the controller gains are designed by solving a set of matrix inequalities. The upper bound of the quadratic cost function is also derived. Finally, simulation examples are applied to illustrate the effectiveness of the proposed design scheme.

86 citations


Proceedings ArticleDOI
14 Jun 2020
TL;DR: This paper proposes to stochastically combine the root of variations with previous pose information, so as to force the model to take the noise into account, and exploits this idea for motion prediction by incorporating it into a recurrent encoder-decoder network with a conditional variational autoencoder block that learns to exploit the perturbations.
Abstract: Human motion prediction, the task of predicting future 3D human poses given a sequence of observed ones, has been mostly treated as a deterministic problem. However, human motion is a stochastic process: Given an observed sequence of poses, multiple future motions are plausible. Existing approaches to modeling this stochasticity typically combine a random noise vector with information about the previous poses. This combination, however, is done in a deterministic manner, which gives the network the flexibility to learn to ignore the random noise. Alternatively, in this paper, we propose to stochastically combine the root of variations with previous pose information, so as to force the model to take the noise into account. We exploit this idea for motion prediction by incorporating it into a recurrent encoder-decoder network with a conditional variational autoencoder block that learns to exploit the perturbations. Our experiments on two large-scale motion prediction datasets demonstrate that our model yields high-quality pose sequences that are much more diverse than those from state-of-the-art stochastic motion prediction techniques.

Journal ArticleDOI
TL;DR: State estimation for a class of hidden semi-Markov jump linear systems governed by a two-layer stochastic process in the discrete-time context with numerically checkable conditions on the existence of the OMD filter is presented.
Abstract: This paper is concerned with state estimation for a class of hidden semi-Markov jump linear systems governed by a two-layer stochastic process in the discrete-time context. A semi-Markov chain and an observed-mode sequence constitute the lower and upper layer of the process, respectively. With the aid of the emission probability, a novel filter, which is dependent both on the elapsed time within the activated mode and on the observed mode instead of the system mode, is constructed and called observed-mode-dependent (OMD) filter. A modified $\sigma$ -error mean square stability ( $\sigma$ -MSS) is proposed by considering the weight of expected operation time in each actual system mode. Based on the new $\sigma$ -MSS, together with a class of Lyapunov functions depending on both the system modes and the corresponding observed ones, numerically checkable conditions on the existence of the OMD filter are presented such that the estimation error system is $\sigma$ -MSS with a prescribed $\mathcal {H}_{\infty }$ disturbance attenuation level. A numerical example is presented to demonstrate the theoretical findings.

Journal ArticleDOI
TL;DR: In this article, the central limit theorem for neural networks with a single hidden layer was proved in the asymptotic regime of simultaneously (a) large numbers of hidden units and (b) large number of stochastic gradient descent training iterations.

Journal ArticleDOI
TL;DR: This work discusses the model’s extinction as well as the stationary distribution in order to derive the sufficient criterion for the persistence and disease’ extinction and the numerical simulation for supporting the theoretical findings.
Abstract: Similar to other epidemics, the novel coronavirus (COVID-19) spread very fast and infected almost two hundreds countries around the globe since December 2019 The unique characteristics of the COVID-19 include its ability of faster expansion through freely existed viruses or air molecules in the atmosphere Assuming that the spread of virus follows a random process instead of deterministic The continuous time Markov Chain (CTMC) through stochastic model approach has been utilized for predicting the impending states with the use of random variables The proposed study is devoted to investigate a model consist of three exclusive compartments The first class includes white nose based transmission rate (termed as susceptible individuals), the second one pertains to the infected population having the same perturbation occurrence and the last one isolated (quarantined) individuals We discuss the model’s extinction as well as the stationary distribution in order to derive the the sufficient criterion for the persistence and disease’ extinction Lastly, the numerical simulation is executed for supporting the theoretical findings

Journal ArticleDOI
TL;DR: The proposed method applies the kernel density estimation to establish an ambiguity set of continuous multivariate probability distributions and the optimization model for the integrated dispatch is formulated as a combination of stochastic and robust optimization problems to solve the integrated energy and reserve dispatch problem with variable and correlated renewable energy generation.
Abstract: This paper proposes a data-driven optimization method to solve the integrated energy and reserve dispatch problem with variable and correlated renewable energy generation. The proposed method applies the kernel density estimation to establish an ambiguity set of continuous multivariate probability distributions and the optimization model for the integrated dispatch is formulated as a combination of stochastic and robust optimization problems. First, a risk-averse two-stage stochastic optimization model is formulated to hedge the distributional uncertainty. Next, the second-stage worst case expectation is evaluated, using the equivalent model reformulation, as a combination of conditional value-at-risk (CVaR) and the extreme cost in the worst case scenario. The CVaR is calculated using a scenario-based stochastic optimization problem. After describing the wind power correlation in ellipsoidal uncertainty sets, the robust optimization problem for finding the worst case cost is cast into a mixed-integer second-order cone programming problem. Finally, the column-and-constraint generation method is employed to solve the proposed risk-averse two-stage problem. The proposed method is tested on the 6-bus and IEEE 118-bus systems and validated by comparing the results with those of conventional stochastic and robust optimization methods.

Journal ArticleDOI
TL;DR: It is shown that the random attack will be able to destroy the stability, therefore, a large feedback gain may be necessary, and almost sure stability is ensured based on Doob's Martingale Convergence Theorem.
Abstract: This article is concerned with the stability problem for a class of Lipschitz-type nonlinear systems in networked environments, which are suffered from random and impulsive deception attacks. The attack is modeled as a randomly destabilizing impulsive sequence, whose impulsive instants and impulsive gains are both random with only the expectations available. Almost sure stability is ensured based on Doob's Martingale Convergence Theorem. Sufficient conditions are derived for the solution of the nonlinear system to be almost surely stable. An example is given to verify the effectiveness of the theoretical results. It is shown that the random attack will be able to destroy the stability, therefore, a large feedback gain may be necessary.

Journal ArticleDOI
TL;DR: In this paper, statistical machine learning theories are proposed to quickly solve the optimal planning for capacitors by comparing the method with the scenario reduction algorithm and the Monte Carlo method in a 33-bus distribution system.
Abstract: Distributed generation and reactive power resource allocation will affect the economy and security of distribution networks. Deterministic scenario planning cannot solve the problem of network uncertainties, which are introduced by intermittent renewable generators and a variable demand for electricity. However, stochastic programming becomes a problem of great complexity when there is a large number of scenarios to be analyzed and when the computational burden has an adverse effect on the programming solution. In this paper, statistical machine learning theories are proposed to quickly solve the optimal planning for capacitors. Various technologies are used: Markov chains and copula functions are formulated to capture the variability and correlation of weather; consumption behavior probability is involved in the weather-sensitive load model; nearest neighbor theory and nonnegative matrix decomposition are combined to reduce the dimensions and scenario scale of stochastic variables; the stochastic response surface is used to calculate the probabilistic power flow; and probabilistic inequality theory is introduced to directly estimate the objective and constraint functions of the stochastic programming model. The effectiveness and efficiency of the proposed method are verified by comparing the method with the scenario reduction algorithm and the Monte Carlo method in a 33-bus distribution system.

Journal ArticleDOI
TL;DR: A sweeping generalization of so-called Thermodynamic Uncertainty Relations is derived, which not only strengthens the bounds but extends their realm of applicability and in many cases prove their optimality, without resorting to large deviation theory or information-theoretic techniques.
Abstract: We introduce a new technique to bound the fluctuations exhibited by a physical system, based on the Euclidean geometry of the space of observables. Through a simple unifying argument, we derive a sweeping generalization of so-called thermodynamic uncertainty relations (TURs). We not only strengthen the bounds but extend their realm of applicability and in many cases prove their optimality, without resorting to large deviation theory or information-theoretic techniques. In particular, we find the best TUR based on entropy production alone. We also derive a periodic uncertainty principle of which previous known bounds for periodic or stationary Markov chains known in the literature appear as limit cases. From it a novel bound for stationary Markov processes is derived, which surpasses previous known bounds. Our results exploit the non-invariance of the system under a symmetry which can be other than time reversal and thus open a wide new spectrum of applications.

Journal ArticleDOI
TL;DR: A comprehensive review of classical random walks and quantum random walks can be found in this paper, where the authors also compare the algorithms based on quantum random walk and classical random walk from the perspective of time complexity.
Abstract: A random walk is known as a random process which describes a path including a succession of random steps in the mathematical space. It has increasingly been popular in various disciplines such as mathematics and computer science. Furthermore, in quantum mechanics, quantum walks can be regarded as quantum analogues of classical random walks. Classical random walks and quantum walks can be used to calculate the proximity between nodes and extract the topology in the network. Various random walk related models can be applied in different fields, which is of great significance to downstream tasks such as link prediction, recommendation, computer vision, semi-supervised learning, and network embedding. In this paper, we aim to provide a comprehensive review of classical random walks and quantum walks. We first review the knowledge of classical random walks and quantum walks, including basic concepts and some typical algorithms. We also compare the algorithms based on quantum walks and classical random walks from the perspective of time complexity. Then we introduce their applications in the field of computer science. Finally we discuss the open issues from the perspectives of efficiency, main-memory volume, and computing time of existing algorithms. This study aims to contribute to this growing area of research by exploring random walks and quantum walks together.

Journal ArticleDOI
TL;DR: The SMC law is constructed to ensure the reachability of the sliding mode dynamics in a finite-time level and one joint of space robot manipulator model is described as nonlinear stochastic S-MSSs to illustrate the validity of the proposed SMC design method.
Abstract: In this paper, the sliding mode control (SMC) design for nonlinear stochastic semi-Markov switching systems (S-MSSs) is studied via the bound of time-varying transition rate matrix, in which semi-Markov switching parameters, stochastic disturbance, uncertainty, and nonlinearity are all considered in a unified framework. The system under consideration is more general, which covers the Markov switching system with sojourn-time-independent transition rate matrix as a special case. Many practical systems subject to unpredictable structural variations can be characterized by nonlinear stochastic S-MSSs with sojourn-time-dependent transition rate matrix. The specific information about the bound of time-varying transition rate matrix is known for the sliding mode controller design. First, by using the stochastic semi-Markov Lyapunov function, sojourn-time-dependent sufficient conditions are developed to guarantee the closed-loop sliding mode dynamics stochastically stable. Then, the SMC law is constructed to ensure the reachability of the sliding mode dynamics in a finite-time level. Finally, one joint of space robot manipulator model is described as nonlinear stochastic S-MSSs to illustrate the validity of the proposed SMC design method.

Journal ArticleDOI
TL;DR: A new data-driven Brownian motion model is proposed that utilizes the adaptive extended Kalman filter (AEKF) parameter identification method and has significant accuracy and robustness for both model adaptability and RUL prediction.
Abstract: Degradation dynamics modeling and health prognosis play extremely important roles in system prognostics and health management. Wiener process-based degradation models and remaining useful life (RUL) prediction methods have the advantage of high flexibility and efficiency, with features such as Brownian motion with drift and scale parameters. They can also quantify prediction uncertainty through inverse Gaussian distribution. However, prior studies use offline-identified model parameters, which can result in difficulties in both model adaptability and health prognosis. To improve the performance of Wiener process models, this article proposes a new data-driven Brownian motion model that utilizes the adaptive extended Kalman filter (AEKF) parameter identification method. The proposed model can update model parameters online and adapt to uncertain degradation operations. This data-driven method has the flexibility and efficiency of Brownian motion models but avoids their shortcomings in model adaptability and health prognosis. The model parameters and drift parameter are online estimated based on AEKF using limited historical system measurements. The effectiveness of the proposed data-driven framework in degradation modeling and RUL prediction is evaluated through simulations and experimental results on lithium-ion battery degradation data. The results show that the proposed approach has significant accuracy and robustness for both model adaptability and RUL prediction.

Journal ArticleDOI
TL;DR: A distribution reconfiguration framework to adapt to the distribution network considering the twofold random and fuzzy uncertainties of the wind, photovoltaic power generation, and load demand and considering the power loss reduction and voltage stability is presented.
Abstract: This paper presents a distribution reconfiguration framework to adapt to the distribution network considering the twofold random and fuzzy uncertainties of the wind, photovoltaic power generation, and load demand and considering the power loss reduction and voltage stability. First, the random fuzzy power output models of distributed generation and load are built based on the random fuzzy theory. Second, the corresponding objective functions are established, which are the random fuzzy expected value of active power loss and maximum probability of voltage limit. Third, the modified particle swarm optimization (MPSO) algorithm based on Kruskal algorithm is introduced for the first time to determine the optimal network topology. The Kruskal algorithm is employed to generate a radial network topology directly without checking the loops and islands. Lastly, the proposed method is applied to the IEEE33, PG&E 69-bus distribution systems, 25-bus unbalanced distribution system, as well as a real 109-bus distribution system. The results show that the proposed method has a good performance to solve distribution network reconfiguration problem.

Journal ArticleDOI
TL;DR: In this paper, the ergodicity breaking parameter EB quantifying the trajectory-to-trajectory fluctuations of the non-Gaussian anomalous diffusion in terms of a random-diffusivity mechanism in the presence of power-law correlated fractional Gaussian noise is studied.
Abstract: Numerous examples for a priori unexpected non-Gaussian behaviour for normal and anomalous diffusion have recently been reported in single-particle tracking experiments. Here, we address the case of non-Gaussian anomalous diffusion in terms of a random-diffusivity mechanism in the presence of power-law correlated fractional Gaussian noise. We study the ergodic properties of this model via examining the ensemble- and time-averaged mean-squared displacements as well as the ergodicity breaking parameter EB quantifying the trajectory-to-trajectory fluctuations of the latter. For long measurement times, interesting crossover behaviour is found as function of the correlation time $\tau$ of the diffusivity dynamics. We unveil that at short lag times the EB parameter reaches a universal plateau. The corresponding residual value of EB is shown to depend only on $\tau$ and the trajectory length. The EB parameter at long lag times, however, follows the same power-law scaling as for fractional Brownian motion. We also determine a corresponding plateau at short lag times for the discrete representation of fractional Brownian motion. These analytical predictions are in excellent agreement with results of computer simulations of the underlying stochastic processes. Our findings can help distinguishing and categorising certain nonergodic and non-Gaussian features of particle displacements, as observed in recent single-particle tracking experiments.

Journal ArticleDOI
TL;DR: A new finite time design method is proposed, which can reduce the difficulty in designing controllers by traditional methods and guarantee that the closed-loop system is semi-global finite-time stable in probability, and the convergence performances are well in presence of actuator quantization.
Abstract: In this article, the problem of the stochastically finite time stabilization for an uncertain single-input and single-output stochastic system in presence of input quantization is studied. The broad learning system (BLS) is first applied to identify the uncertain system with unknown dynamics. The problem of unmeasured states can be solved by establishing a novel BLS-based state observer. Combining the stochastically finite time theorem with ${\rm {It\hat{o}}}$ formula, a new finite time design method is proposed, which can reduce the difficulty in designing controllers by traditional methods. A stochastically finite time quantized control method is presented by utilizing a new finite time design Lemma 3 and quantized input decomposition technique. The developed control approach can guarantee that the closed-loop system is semi-global finite-time stable in probability, and the convergence performances are well in presence of actuator quantization. The simulation on a chemical reactor is utilized to verify the proposed scheme, which demonstrates the advantage of BLS, as well as the validity of our control method.

Journal ArticleDOI
20 Apr 2020
TL;DR: This work proves a generalized extension theorem that applies to all theories of stochastic processes, putting them on equally firm mathematical ground as their classical counterpart, and shows that quantum causal modelling and quantum stochastics processes are equivalent.
Abstract: In classical physics, the Kolmogorov extension theorem lays the foundation for the theory of stochastic processes. It has been known for a long time that, in its original form, this theorem does not hold in quantum mechanics. More generally, it does not hold in any theory of stochastic processes -- classical, quantum or beyond -- that does not just describe passive observations, but allows for active interventions. Such processes form the basis of the study of causal modelling across the sciences, including in the quantum domain. To date, these frameworks have lacked a conceptual underpinning similar to that provided by Kolmogorov's theorem for classical stochastic processes. We prove a generalized extension theorem that applies to all theories of stochastic processes, putting them on equally firm mathematical ground as their classical counterpart. Additionally, we show that quantum causal modelling and quantum stochastic processes are equivalent. This provides the correct framework for the description of experiments involving continuous control, which play a crucial role in the development of quantum technologies. Furthermore, we show that the original extension theorem follows from the generalized one in the correct limit, and elucidate how a comprehensive understanding of general stochastic processes allows one to unambiguously define the distinction between those that are classical and those that are quantum.

Journal ArticleDOI
TL;DR: This paper deals with the anti-synchronization issue for stochastic delayed reaction-diffusion neural networks subject to semi-Markov jump parameters, and a resilient fault-tolerant controller is utilized to ensure theAnti- Synchronization in the presence of actuator failures as well as gain perturbations, simultaneously.

Journal ArticleDOI
TL;DR: A novel nonlinear fault compensation function with adjustable parameter factor is first introduced to establish a standard adaptive fault-tolerant control (AFTC) strategy based on the mean-value theorem to surmount the design difficulty from nonaffine nonlinear term with multi-input and single-output (MISO) faulty modes.
Abstract: In this article, the adaptive fault-tolerant tracking control problem of nonaffine stochastic nonlinear systems with actuator failures and full-state constraints is studied. To surmount the design difficulty from nonaffine nonlinear term with multi-input and single-output (MISO) faulty modes, a novel nonlinear fault compensation function with adjustable parameter factor is first introduced to establish a standard adaptive fault-tolerant control (AFTC) strategy based on the mean-value theorem. Then, the remaining nonlinear function, including the partial loss of effectiveness, outage, and stuck cases, together with the constructed compound nonlinear function can be approximated by using the suitable fuzzy-logic system (FLS). Moreover, it is shown that all the states of nonaffine stochastic nonlinear systems are not violating the preset constraint bounds by employing the barrier Lyapunov functions (BLFs). Also, the given adaptive controller can guarantee all the closed-loop signals are uniformly ultimately bounded (UUB) in probability in the sense of fourth-moment within the appropriate compact sets. Finally, two simulation examples are given to demonstrate the validity of the proposed method.

Journal ArticleDOI
TL;DR: The fuzzy asynchronous dissipative filtering issue for Markov jump discrete-time nonlinear systems subject to fading channels is discussed in this paper, where the Rice fading model is employed to characterize the fading channels phenomenon in the system measurements for the first time.
Abstract: The fuzzy asynchronous dissipative filtering issue for Markov jump discrete-time nonlinear systems subject to fading channels is discussed in this paper, where the Rice fading model is employed to characterize the fading channels phenomenon in the system measurements for the first time. The attention is focused on developing an available asynchronous filter, which can ensure that the underlying error system is dissipative. In this regard, several important performances can be investigated conveniently by introducing adjustment matrices. By means of the stochastic analysis theory and the network control technique, some sufficient conditions for the solvability of the addressed problem are presented, simultaneously, the gains of the filter desired are determined correspondingly. An illustrative example is finally exploited to explain the utilizability of the developed approach.

Journal ArticleDOI
TL;DR: It is shown that under the same decay rate, the dynamic event-generators may further reduce the conservatism than their static counterparts and Riccati-like conditions for global mean square exponential stability of linear stochastic systems under dynamic ETC are established.
Abstract: This technical note discusses the stability analysis and design procedure of event-triggered control (ETC) for nonlinear stochastic systems with state-dependent noise. Periodic event-generators and continuous event-generators are considered in both static and dynamic cases. All the event-generators we proposed have a guaranteed positive minimum interevent time for every sample path solution of the systems. It is shown that under the same decay rate, the dynamic event-generators may further reduce the conservatism than their static counterparts. In addition, Riccati-like conditions for global mean square exponential stability of linear stochastic systems under dynamic ETC are established. The theoretical results are illustrated by means of a numerical example.

Journal ArticleDOI
TL;DR: By using stochastic analysis techniques and algebra graph theory, it is shown that the cooperative control problem under consideration is solvable and the errors between the followers’ outputs and the leader’s output can be made arbitrarily small while keeping all states of the closed-loop system bounded in probability.
Abstract: This paper studies the cooperative control problem of multiple nonlinear benchmark systems perturbed by second-order moment processes. The nonlinear benchmark system consists of a moving car and a rolling ball in oscillating surroundings. When the leader is only accessible to a small part of the followers in a directed graph, a new vectorial backstepping method is proposed for the design of distributed cooperative control laws. By using stochastic analysis techniques and algebra graph theory, it is shown that the cooperative control problem under consideration is solvable. Specifically, the errors between the followers’ outputs and the leader’s output can be made arbitrarily small while keeping all states of the closed-loop system bounded in probability. Finally, the effectiveness of the proposed control scheme is demonstrated through a simulation example.