Stochastic Sampled-data Research Articles

Fault-Tolerant Stochastic Sampled-Data Fuzzy Control for Nonlinear Delayed Parabolic PDE Systems

For nonlinear delayed parabolic partial differential equation (PDE) systems, this paper addresses fault-tolerant stochastic sampled-data (SD) fuzzy control under spatially point measurements (SPMs). Initially, a T–S fuzzy PDE model is given to accurately describe the nonlinear delayed parabolic PDE system. Secondly, in consideration of possible actuator failure, a fault-tolerant SD fuzzy controller with stochastic sampling under SPMs is designed for nonlinear delayed parabolic PDE system, where two sampling periods are considered whose occurrence probabilities are given constants and satisfy the Bernoulli distribution. Then, by constructing a novel time-dependent Lyapunov functional, sufficient conditions that guarantee the mean square exponential stability of closed-loop delayed PDE system are obtained based on linear matrix inequalities (LMIs). Lastly, three examples are given to illustrate the designed approach.

Reachable set estimation and stochastic sampled-data exponential synchronization of Markovian jump neural networks with time-varying delays

In this paper, the stochastic sampled-data exponential synchronization problem for Markovian jump neural networks (MJNNs) with time-varying delays and the reachable set estimation (RSE) problem for MJNNs subjected to external disturbances are investigated. Firstly, assuming that two sampled-data periods satisfy Bernoulli distribution, and introducing two stochastic variables to represent the unknown input delay and the sampled-data period respectively, the mode-dependent two-sided loop-based Lyapunov functional (TSLBLF) is constructed, and the conditions for the mean square exponential stability of the error system are derived. Furthermore, a mode-dependent stochastic sampled-data controller is designed. Secondly, by analyzing the unit-energy bounded disturbance of MJNNs, a sufficient condition is proved that all states of MJNNs are confined to an ellipsoid under zero initial condition. In order to make the target ellipsoid contain the reachable set of the system, a stochastic sampled-data controller with RSE is designed. Eventually, two numerical examples and an analog resistor–capacitor network circuit are provided to show that the textual approach can obtain a larger sampled-data period than the existing approach.

Event-triggered group consensus for one-sided Lipschitz multi-agent systems with input saturation

This paper investigates event-triggered group consensus problem for multi-agent systems with input saturation under fixed topology and Markovian switching topologies respectively. The agent dynamics is described by one-sided Lipschitz nonlinear function, which covers a broad family of nonlinear systems and includes the well-known Lipschitz system as a special case. A novel distributed dynamic event-triggered communication scheme is proposed based on the local stochastic sampling information among the agents, which includes some existing schemes as special cases. A new stochastic sampled-data dependent error system is obtained by model transformation, based on the discontinuous Lyapunov stability theory, some local group consensus criteria in mean square can be derived for fixed topology and Markovian switching topologies, respectively. Moreover, an optimization algorithm is introduced to estimate the region of initial conditions. Finally, two specific numerical examples are employed to illustrate the effectiveness of the theoretical results.

Stochastic Sampled-Data Exponential Synchronization of Markovian Jump Neural Networks With Time-Varying Delays.

In this article, the exponential synchronization of Markovian jump neural networks (MJNNs) with time-varying delays is investigated via stochastic sampling and looped-functional (LF) approach. For simplicity, it is assumed that there exist two sampling periods, which satisfies the Bernoulli distribution. To model the synchronization error system, two random variables that, respectively, describe the location of the input delays and the sampling periods are introduced. In order to reduce the conservativeness, a time-dependent looped-functional (TDLF) is designed, which takes full advantage of the available information of the sampling pattern. The Gronwall-Bellman inequalities and the discrete-time Lyapunov stability theory are utilized jointly to analyze the mean-square exponential stability of the error system. A less conservative exponential synchronization criterion is derived, based on which a mode-independent stochastic sampled-data controller (SSDC) is designed. Finally, the effectiveness of the proposed control strategy is demonstrated by a numerical example.

Adaptive dynamic event-triggered cluster synchronization in an array of coupled neural networks subject to cyber-attacks

This paper is concerned with cluster synchronization in an array of coupled neural networks subject to cyber-attacks, where a random variable is employed to reflect the success ration of the launched cyber-attacks. To save the energy consumption and alleviate the transmission load of the network, a novel adaptive distributed dynamic event-triggered communication scheme is presented based on the local stochastic the state sampling information, compared with some existing results, the different event-triggered matrices and auxiliary variables are introduced for each node to adjust its threshold dynamically, which can further reduce the sampled-data transmission, the proposed event-triggered scheme includes some existing event-triggered schemes as special cases. The cluster synchronization controllers are designed based on the states of neighboring nodes at event-triggered instants, a new stochastic sampled-data dependent error model is constructed, some mean-square cluster synchronization criteria can be derived by the Lyapunov stability theory and algebraic graph theory, and the feedback matrices and event-triggered matrices can be obtained by solving some linear matrix inequalities. Finally, two numerical examples are employed to show the validity and advantage of the theoretical results.

Adaptive event-triggered group consensus of multi-agent systems under stochastic sampling

This paper investigates group consensus for linear multi-agent systems with nonidentical dynamics. A novel adaptive event-triggered communication scheme is presented by using the stochastic sampling information, the event-triggered matrices and time-varying event-triggered parameters are introduced into event-triggered condition, where event-triggered parameters can be adjusted with the system dynamics evolving. The group consensus protocol is designed based on the neighboring agents information at event-triggered instants, then a new stochastic sampled-data dependent error model is constructed, some group consensus criteria in mean-square can be derived and the feedback matrices can also be obtained. Finally, two numerical examples are provided to illustrate the validity of the theoretical results.

Consensus Protocol Design for Leader-Following Multi-Agent Systems With Stochastic Sampling Information

Abstract This paper studies a consensus protocol design for leader-following multi-agent systems (MASs) via stochastic sampling information. Unlike traditional sampled-data control, this paper is focused on the stochastically varying sample intervals with a given probability by the Bernoulli distribution. Based on the Lyapunov–Krasovskii functional and reciprocally convex technique, the sufficient conditions are derived for the stochastic sampled-data protocol design of the error system, which guarantees that the following agent's states can reach an agreement on the leader's state. Finally, the numerical examples are provided to demonstrate the effectiveness of the developed theoretical results.

Synchronization of Delayed Neural Networks With Actuator Failure Based on Stochastic Sampled-Data Controller

This paper addresses the master-slave synchronization problems of delayed neural networks with actuator failure based on stochastic sampled-data controller. To simplify the analysis process, only two different sampling periods whose occurrence probabilities follow the Bernoulli distribution are considered. In addition, it can be further extended to cases with multiple random sampling periods. The sampling system with random parameters is transformed into a continuous system through applying the input delay method. The novelty of this article is to consider the problem of actuator failure which may exist in the real world. By constructing a new type of Lyapunov-Krasovskii function (LKF), a sampling controller for neural networks synchronization system is designed. Using Jensens's inequality, Wirtinger's inequality and convex optimization methods, the stability criterion of neural networks with low conservativeness is acquired. Meanwhile, the controller gain matrix can be obtained through solving the linear matrix inequalities (LMIs). One numerical example provides feasibility and advantages of theoretical results.

Stochastic sampled‐data controller for T–S fuzzy chaotic systems and its applications

The present study mainly focuses on designing a stochastic sampled-data controller for chaotic Takagi–Sugeno (T–S) fuzzy systems. Distinct to the existing controller schemes, in this work, the random time delay is introduced into the proposed control scheme that ensures the exponential stabilisation of T–S fuzzy models. In addition, the input delays are assumed to be randomly time-varying, which copes with the traditional uncorrelated Bernoulli distributed sequences. Based on the proposed Lyapunov–Krasovskii functional and using new weighted integral inequalities, the stability and stabilisation conditions are derived and expressed in terms of linear matrix inequalities, which ensure the exponential stability of the states. Finally, in the simulation results, the chaotic nature of two dynamical systems are considered for validation of the derived conditions. From the simulation results, it is concluded that the proposed method can provide better stability performance and less conservative results.

State Estimation for Coupled Output Complex Dynamical Networks with Stochastic Sampled-Data

In this paper, the problem of the state estimation on complex dynamical networks coupled with stochastically sampling is studied. By using the input delay approach, the sampled-data system is transformed into a time-continuous system where the data at sampling periods have two different time-varying delays randomly happening between two intervals which have different known lower and upper bounds. The sampling points occur with two known probabilities and satisfy Bernoulli distribution. There are two different types of stochastically-sampled-data considered in this complex dynamical network. One of the stochastically-sampled-data is used to data exchange over the dynamical network, the other is used to construct the Luenburger state estimator as feedback data. We derive the state estimator for the complex dynamical network with new models which combined with two types of above stochastic-sampled-data, and delay-dependent asymptotical stabilities of the estimation error has been solved by constructing a Lyapunov–Krasovskii functional and the linear matrix inequality toolbox in MATLAB. Finally, a numerical example has been illustrated to demonstrate the effectiveness of the proposed results.

Modeling and tracker for unknown nonlinear stochastic delay systems with positive input constraints

An approach for universal modeling and tracker design for input-constrained unknown nonlinear input time-delay stochastic sampled-data systems is newly proposed in this paper. First, the improved observer/Kalman filter identification (OKID) method, which uses the current output measurement to estimate the current state, is newly proposed in this paper and it is shown that it outperforms the traditional OKID method. In addition, it is shown that the newly proposed current output-based Kalman filter is a well-performed output estimator in the extreme case, in which it is not a filter anymore, becoming a universal way of formulating an artificial system model of a real physical process without disturbing its normal operation. Consequently, the proposed artificial system model has the following advantages: (i) It is capable of quantifying the stochastic and deterministic characteristics of the dynamical system of interest; (ii) It is capable of carrying out the analyses of various control-design methodologies to achieve the performance specifications in the pre-study phase; and (iii) It is capable of estimating missing and/or abnormal output measurements during the testing and/or practical operating phases. Furthermore, an alternative re-designed current output-based observer is newly proposed in this paper, in order to develop a modified observer-based model predictive control (MPC) with input constraints to improve the performance of the unknown nonlinear time-delay stochastic system. When the proposed artificial system model is used together with the proposed constrained MPC, a long-time prediction of future input–output sets in a closed-loop setting can be carried out. Finally, the operation of a temperature controlled real nonlinear input time-delay blast furnace process is presented as a case study in this paper, to show the effectiveness of the proposed mechanism.

H ∞ control for a class of multi‐agent systems via a stochastic sampled‐data method

In this study, the stochastic sampled-data approach is developed to deal with the H ∞ control problem for a class of linear multi-agent systems. For each agent, signals should be transmitted to the control input, including not only its own measurements, but also the output information received from the neighbour agents. The relationships of information communications between the whole multi-agents are totally reflected by a weighted directed graph with a fixed topology structure. To the addressed problem, the author's focus is to design an output feedback controller for each agent such that, for the external energy bounded disturbances, the exponential stability in the mean square sense and interference rejection ability under consideration can be guaranteed. By assuming that the sampling period of each agent switches between two values in a probabilistic way, the stochastic sampling phenomenon is well characterised in every sampling tasks. In virtue of Lyapunov theory and semi-definite programming method, sufficient conditions are derived to ensure the exponential stability as well as H ∞ performance, and the feedback controllers are also designed by solving some certain matrix inequalities. Finally, a numerical simulation is given to demonstrate the validness of the proposed control strategy.

Stochastic Sampled-Data Control for H∞ Stabilization of Transport Reaction Systems

This paper investigates the problem of stochastic sampled-data H∞ control for a class of parabolic systems governed by one-dimensional semilinear transport reaction systems with external disturbances. A sampled-data controller design is developed by introducing the time-varying delay in the control input signals. The m sampling periods are considered whose occurrence probabilities are known constants and satisfy Bernoulli distribution. Since discontinuous Lyapunov functional copes well with problems of sampled-data control systems, a discontinuous Lyapunov functional is constructed based on the extended Wirtinger’s inequality. With this new approach, sufficient conditions that guarantee the asymptotic mean-square stabilization of the considered systems and the L2-gain analysis are derived in terms of linear matrix inequalities (LMIs), which can be solved by any of the available software.

Event‐triggered consensus of Markovian jumping multi‐agent systems via stochastic sampling

This study investigates the issue of mean square consensus for multiple agents connected by a directed network. The graph of the network is supposed to have a spanning tree and each agent is taken as a Markovian jumping system. By utilising the event-triggered strategy, some sufficient conditions for consensus are presented whether the transition rates for the Markov chain being completely known or not. Furthermore, the event-triggered function designed in this study is dependent on the stochastic sampled-data from neighbouring agents. Theoretical results are provided according to the graph theory, Lyapunov functional and linear matrix inequality approach. Finally, a numerical example is given to demonstrate the effectiveness of the theoretical analysis.

Stochastic sampled-data H∞ synchronization of coupled neutral-type delay partial differential systems

This paper discusses the asymptotical synchronization and H∞ synchronization of coupled neutral-type delay partial differential systems (NDPDSs). A sampled-data controller with m stochastically varying sampling periods whose occurrence probabilities are given constants is considered. By using the method of a nonsingular matrix transformation, we decouple the coupled error dynamical systems. Then, sufficient conditions that guarantee the asymptotic stability of decoupled synchronization error dynamical systems are derived in terms of linear matrix inequalities (LMIs) by constructing a suitable Lyapunov–Krasovskii functional with triple integral terms and by using Jensen׳s inequality and reciprocally convex combination technique, which implies the asymptotical synchronization of the coupled NDPDSs. Moreover, the stability criteria for the H∞ stabilization of decoupled synchronization error dynamical systems with external disturbances are also derived in terms of LMIs, which guarantee the H∞ synchronization of the coupled NDPDSs. The equivalence between the H∞ stability of decoupled synchronization error dynamical systems and the H∞ synchronization of coupled NDPDSs is also proved by mathematical analysis. Finally, numerical examples are provided to demonstrate the effectiveness of the obtained results.

Synchronization of Neural Networks With Control Packet Loss and Time-Varying Delay via Stochastic Sampled-Data Controller.

This paper addresses the problem of exponential synchronization of neural networks with time-varying delays. A sampled-data controller with stochastically varying sampling intervals is considered. The novelty of this paper lies in the fact that the control packet loss from the controller to the actuator is considered, which may occur in many real-world situations. Sufficient conditions for the exponential synchronization in the mean square sense are derived in terms of linear matrix inequalities (LMIs) by constructing a proper Lyapunov-Krasovskii functional that involves more information about the delay bounds and by employing some inequality techniques. Moreover, the obtained LMIs can be easily checked for their feasibility through any of the available MATLAB tool boxes. Numerical examples are provided to validate the theoretical results.

Leader-following consensus for networked multi-teleoperator systems via stochastic sampled-data control

In this paper, the leader-following consensus problem is investigated for a networked multi-teleoperator system (NMTS) under a stochastic sampled-data controller. By utilizing the input delay approach, the sampling period is transformed into a time-varying yet bounded delay. With the help of algebraic graph theory and probability theory, a new consensus protocol is designed. Subsequently, a sufficient condition for the leader-following consensus of NMTS is derived in the form of linear matrix inequality (LMI) by constructing an appropriate Lyapunov–Krasovskii functional and by utilizing some matrix and integral inequality techniques. Based on the derived condition, the design method of the desired sampled-data controller is also obtained in terms of the solution to LMI which can be checked effectively by using available software. In addition, the effectiveness of the obtained theoretical results is illustrated by a numerical example.

Stochastic Sampled-Data Control for Exponential Synchronization of Markovian Jumping Complex Dynamical Networks with Mode-Dependent Time-Varying Coupling Delay

In this paper, we address the problem of exponential synchronization of Markovian jumping complex dynamical networks with mode-dependent time-varying coupling delay via a stochastic sampled-data controller. In addition, the sampling period is assumed to be time-varying and switches between $$m$$ m different values in a random way with given probability. By constructing a new Lyapunov---Krasovskii functional (LKF) with triple integral terms and by employing convex combination technique and free weighting matrices method, sufficient conditions for the coupled complex dynamical network to be globally exponentially synchronized in the mean square sense are derived. The information about the lower bound of the discrete time-varying delay is used in the LKF. Based on the derived condition, the desired sampled-data feedback controller is designed in terms of the solution to linear matrix inequalities. Finally, two numerical examples are given to illustrate the effectiveness of the proposed methods.

A Stochastic Sampled-Data Approach to Distributed $H_{\infty }$ Filtering in Sensor Networks

In this paper, the problem of distributed <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filtering in sensor networks using a stochastic sampled-data approach is investigated. A set of general nonlinear equations described by sector-bounded nonlinearities is utilized to model the system and sensors in networks. Each sensor receives the information from both the system and its neighbors. The signal received by each sensor is sampled by a sampler separately with stochastic sampling periods before it is employed by the corresponding filter. By converting the sampling periods into bounded time-delays, the design problem of the stochastic sampled-data based distributed <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filters amounts to solving the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filtering problem for a class of stochastic nonlinear systems with multiple bounded time-delays. Then, by constructing a new Lyapunov functional and employing both the Gronwall's inequality and the Jenson integral inequality, a sufficient condition is derived to guarantee the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> performance as well as the exponential mean-square stability of the resulting filtering error dynamics. Subsequently, the desired sampled-data based distributed <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filters are designed in terms of the solution to certain matrix inequalities that can be solved effectively by using available software. Finally, a numerical simulation example is exploited to demonstrate the effectiveness of the proposed sampled-data distributed <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> filtering scheme.

Low-order self-tuner for fault-tolerant control of a class of unknown nonlinear stochastic sampled-data systems

Based on the modified state-space self-tuning control (STC) via the observer/Kalman filter identification (OKID) method, an effective low-order tuner for fault-tolerant control of a class of unknown nonlinear stochastic sampled-data systems is proposed in this paper. The OKID method is a time-domain technique that identifies a discrete input–output map by using known input–output sampled data in the general coordinate form, through an extension of the eigensystem realization algorithm (ERA). Then, the above identified model in a general coordinate form is transformed to an observer form to provide a computationally effective initialization for a low-order on-line “auto-regressive moving average process with exogenous (ARMAX) model”-based identification. Furthermore, the proposed approach uses a modified Kalman filter estimate algorithm and the current-output-based observer to repair the drawback of the system multiple failures. Thus, the fault-tolerant control (FTC) performance can be significantly improved. As a result, a low-order state-space self-tuning control (STC) is constructed. Finally, the method is applied for a three-tank system with various faults to demonstrate the effectiveness of the proposed methodology.