Stochastic Sampled-data Control Research Articles

Finite-time H∞ synchronization of semi-Markov jump neural networks with two delay components with stochastic sampled-data control

This article investigates the finite-time H∞ synchronization for semi-Markov jump neural networks with two delay components based on stochastic sampled data control. Additionally, the parametric uncertainties are randomly varying which follows the Bernoulli distributed sequences. In the stochastic sampled data control, the sampling interval ′m′ is supposed to be two different values in the time-varying component with given probability conditions. By constructing triple and quadruple integral term in the Lyapunov-Krasovskii functional (LKF) a new integral inequality technique is addressed to derive the main results. Dissimilar from previous literature, involving the new integral inequality, a delay dependent finite-time H∞ synchronization requirements are acquired with regard to linear matrix inequalities (LMIs). In the end, the effectiveness of the considered stochastic sampled data control finite time synchronization scheme is highlighted by numerical examples.

Exponential State Estimation for Delayed Competitive Neural Network Via Stochastic Sampled-Data Control with Markov Jump Parameters Under Actuator Failure

Abstract This article examines the problem of estimating the states of Markovian jumping competitive neural networks, where the estimation is done using stochastic sampled-data control with time-varying delay. Instead of continuously measuring the states, the network relies on sampled measurements, and a sampled-data estimator is proposed. The estimator uses probabilistic sampling during two sampling periods, following a Bernoulli distribution. The article also takes into account the possibility of actuator failure in real systems. To ensure the exponentially mean-square stability of the delayed neural networks, the article constructs a Lyapunov-Krasovskii functional (LKF) that includes information about the bounds of the delay. The sufficient conditions for stability are derived in the form of linear matrix inequalities (LMIs) by employing modified free matrix-based integral inequalities. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed method.

Stochastic sampled-data multi-objective control of active suspension systems for in-wheel motor driven electric vehicles

This paper addresses the sampled-data multi-objective active suspension control problem for an in-wheel motor driven electric vehicle subject to stochastic sampling periods and asynchronous premise variables. The focus is placed on the scenario that the dynamical state of the half-vehicle active suspension system is transmitted over an in-vehicle controller area network that only permits the transmission of sampled data packets. For this purpose, a stochastic sampling mechanism is developed such that the sampling periods can randomly switch among different values with certain mathematical probabilities. Then, an asynchronous fuzzy sampled-data controller, featuring distinct premise variables from the active suspension system, is constructed to eliminate the stringent requirement that the sampled-data controller has to share the same grades of membership. Furthermore, novel criteria for both stability analysis and controller design are derived in order to guarantee that the resultant closed-loop active suspension system is stochastically stable with simultaneous H2 and H∞ performance requirements. Finally, the effectiveness of the proposed stochastic sampled-data multi-objective control method is verified via several numerical cases studies in both time domain and frequency domain under various road disturbance profiles.

Security control of Markovian jump neural networks with stochastic sampling subject to false data injection attacks★ ★This work was supported by the NNSF of China under Grants 61973199, 62003794, 62173214, the Shandong Provincial NSF ZR2020QF050, ZR2021MF003.

The security control of Markovian jumping neural networks (MJNNs) is investigated under false data injection attacks that take place in the shared communication network. Stochastic sampled-data control is employed to research the exponential synchronization of MJNNs under false data injection attacks (FDIAs) since it can alleviate the impact of the FDIAs on the performance of the system by adjusting the sampling periods. A multi-delay error system model is established through the input-delay approach. To reduce the conservatism of the results, a sampling-period-probability-dependent looped Lyapunov functional is constructed. In light of some less conservative integral inequalities, a synchronization criterion is derived, and an algorithm is provided that can be solved for determining the controller gain. Finally, a numerical simulation is presented to confirm the efficiency of the proposed method.

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.

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.

Exponential state estimation for competitive neural network via stochastic sampled-data control with packet losses

This paper investigates the exponential state estimation problem for competitive neural networks via stochastic sampled-data control with packet losses. Based on this strategy, a switched system model is used to describe packet dropouts for the error system. In addition, transmittal delays between neurons are also considered. Instead of the continuous measurement, the sampled measurement is used to estimate the neuron states, and a sampled-data estimator with probabilistic sampling in two sampling periods is proposed. Then the estimator is designed in terms of the solution to a set of linear matrix inequalities (LMIs), which can be solved by using available software. When the missing of control packet occurs, some sufficient conditions are obtained to guarantee that the exponentially stable of the error system by means of constructing an appropriate Lyapunov function and using the average dwell-time technique. Finally, a numerical example is given to show the effectiveness of the proposed method.

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.

New result on reliable [formula omitted] performance state estimation for memory static neural networks with stochastic sampled-data communication

This work examines the H∞ performance state estimation problem for memory static neural networks (MSNNs) with reliable state feedback stochastic sampled-data control (SSDC). The purpose of presenting this study is to determine whether the H∞ performance and criteria with less conservatism for stability could be gained by SSDC for MSNNs or not. Firstly, we suppose that the sampling interval values follow Bernoulli distribution and the probability of occurrence are teadfast constant, then generalize it to a more universal form. Secondly, on basis of considering the sampling input delay and its sawtooth structure characteristics, a modified augmented Lyapunov-Krasovskii functional (LKF) is constructed on account of the free-matrix-based integral inequality (FMBII) together with generalized free-weighting-matrix (GFWM) inequality, which can reduce the conservatism of H∞ performance criteria. Thirdly, the expected estimator gain matrix can be designed in the light of the solution to linear matrix inequalities (LMIs). Finally, an numerical example is given to check the superiority of the proposed MSNNs control design technique.

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.

Pinning stochastic sampled-data control for exponential synchronization of directed complex dynamical networks with sampled-data communications

This paper is concerned with the exponential synchronization of directed complex dynamical networks (CDNs) with sampled-data communications (SDCs) via pinning stochastic sampled-data control. Different from traditional directed CDNs with determined sampling intervals, multiple stochastic varying sampling intervals with given probabilities are considered in this paper. Compared with some existing control schemes, our control method is more practical because the random sampling intervals always happen in some practical situation. In addition, a Lyapunov–Krasovskii functional (LKF) with some new terms is constructed, which can fully capture the information on stochastic sampling intervals, stochastic input delays, and nonlinear functions. Based on the LKF and Wirtinger’s inequality, less conservative synchronization criteria are obtained. Finally, numerical examples are given to illustrate the effectiveness and superiorities of the proposed results.

New approach on designing stochastic sampled-data controller for exponential synchronization of chaotic Lur’e systems

This paper investigates the problem of designing stochastic sampled-data controller for exponential synchronization of chaotic Lur’e systems (CLSs) via a new approach. Specially, first, multiple stochastic sampling intervals with given probabilities are considered and satisfy Bernoulli distribution. Second, unlike other studies, a unified probability framework, which takes sampling interval and time-varying delay into account, is proposed for the first time to design the controller. Based on this unified probability framework, an augmented Lyapunov–Krasovskii functional (LKF) with some new terms is constructed, which can take full advantage of the available information on actual sampling pattern. Different from some existing LKFs needing to be positive definite on the whole sampling intervals, by the new inequality in Lemma 1, the LKF is positive definite only requiring to be positive definite at sampling times. Third, less conservative synchronization criterion is derived and the desired stochastic sampled-data controller is designed. Finally, numerical simulations of Chua’s circuit and neural network are provided to show the effectiveness and advantages of the proposed results.

Stabilization for sampled-data systems under noisy sampling interval

In engineering practice, the sampling interval for a sampled-data system often fluctuates around a nominal/ideal value based on certain probability distributions that can be specified a priori through statistical tests. In this paper, a fundamental stabilization problem is investigated for a class of sampled-data systems under noisy sampling interval. The stochastic sampled-data control system under consideration is first converted into a discrete-time system whose system matrix is represented as an equivalent yet tractable form via the matrix exponential computation. Then, by introducing a Vandermonde matrix, the mathematical expectation of the quadratic form of the system matrix is computed. By recurring to the Kronecker product operation, the sampled-data stabilization controller is designed such that the closed-loop system is stochastically stable in the presence of noisy sampling interval. Subsequently, a special case is considered where the sampling interval obeys the continuous uniform distribution and the corresponding stabilization controller is designed. Finally, a numerical simulation example is provided to demonstrate the effectiveness of the proposed design approach.

On designing stochastic sampled-data controller for master–slave synchronization of chaotic Lur’e system via a novel integral inequality

This study investigates the problem of designing stochastic sampled-data controller for master–slave synchronization of chaotic Lur’e systems (CLSs) via a novel approach. Specially, first, we assume that the occurrence probabilities of the sampling intervals are fixed constants and satisfy a Bernoulli distribution. In order to take full advantage of the sawtooth structure characteristics of the sampling input delay, we construct a newly augmented Lyapunov–Krasovskii functional (LKF) based on the extended Wirtinger inequality. Second, by using a novel free-matrix-based integral inequality (FMBII) including well-known integral inequalities as special cases, an exponentially mean-square synchronization criterion is proposed for analyzing the corresponding synchronization error system. Third, the desired estimator gain can be designed in terms of the solution to linear matrix inequalities (LMIs) which can be solved effectively by using available software. Finally, three numerical simulation examples of Chua’s circuit and neural network are given to illustrate the effectiveness and superiorities of the proposed method.

Robust stochastic sampled-data control for offshore steel jacket platforms with non-linear perturbations

This paper deals with the problem of robust exponential stabilization of offshore steel jacket platforms, where linear fractional uncertainties and randomly occurring uncertainties are taken into account. In this work, we introduce a sampled-data controller with m stochastically varying sampling intervals whose occurrence probabilities are given constants and satisfy Bernoulli distribution. A discontinuous type Lyapunov-Krasovskii functional with triple integral terms based on the extended writinger's inequality is constructed and some sufficient conditions that guarantee the exponential stabilization of considered system are derived in terms of linear matrix inequalities by using Jensen's inequality and reciprocally convex technique. Finally, a numerical example is presented to show the effectiveness of the proposed results.

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.

Robust Stochastic Sampled-Data H∞ Control for a Class of Mechanical Systems With Uncertainties

This paper considers a class of mechanical systems with uncertainties appearing in all the mass, damping, and stiffness matrices. Two cases, linear fractional and randomly occurring uncertainty formulations, are considered. Since sampled-data controllers have an advantage of implementing with microcontroller or digital computer to lower the implementation cost and time, a robust stochastic sampled-data controller is considered with m sampling intervals whose occurrence probabilities are given constants and satisfy Bernoulli distribution. A discontinuous type Lyapunov functional based on the extended Wirtinger's inequality is constructed with triple integral terms and sufficient conditions that promises the robust mean square asymptotic stability of the concerned system are derived in terms of linear matrix inequalities (LMIs). In an aim to reduce the conservatism, a newly introduced concept called the second-order reciprocally convex approach is employed in deriving the bound for some cross terms that arise while maneuvering the derivative of Lyapunov functional. The obtained LMIs can be easily solved through any of the standard available software. Finally, numerical examples are given to verify the effectiveness of the proposed theoretical 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 synchronization of complex dynamical networks with control packet loss and additive time-varying delays

This study examines the exponential synchronization of complex dynamical networks with control packet loss and additive time-varying delays. Additionally, sampled-data controller with time-varying sampling period is considered and is assumed to switch between m different values in a random way with given probability. Then, a novel Lyapunov–Krasovskii functional (LKF) with triple integral terms is constructed and by using Jensen’s inequality and reciprocally convex approach, sufficient conditions under which the dynamical network is exponentially mean-square stable are derived. When applying Jensen’s inequality to partition double integral terms in the derivation of linear matrix inequality (LMI) conditions, a new kind of linear combination of positive functions weighted by the inverses of squared convex parameters appears. In order to handle such a combination, an effective method is introduced by extending the lower bound lemma. To design the sampled-data controller, the synchronization error system is represented as a switched system. Based on the derived LMI conditions and average dwell-time method, sufficient conditions for the synchronization of switched error system are derived in terms of LMIs. Finally, numerical example is employed to show the effectiveness of the proposed methods.