Mean-square Asymptotic Stability Research Articles

Quantized feedback control of distributed radar system with packet dropouts and time-varying delays described by 2D system

In this paper, we present quantized state feedback control for the distributed radar with packet dropouts and time-varying delays. The measurements of state signal are quantized by logarithmic quantizer before being communicated. The measurements missing and time delay often occur due to the communication channel failure. The data missing phenomena was modeled by a Bernoulli distributed stochastic variable taking values of 1 and 0, the delays are time-varying. Firstly, the quantized state feedback control design is transformed into stability analysis for a 2D stochastic system. Secondly, we obtain the stability condition based on linear matrix inequality (LMI) of mean-square asymptotic stability of the 2D stochastic system. Additionally, a quantized state feedback controller is designed based on the linear matrix inequality theorem to meet the environmental requirements of the distributed radar system. Compared to existing methods, the proposed controller designed under this method demonstrates robustness and stability in addressing the three challenges of packet loss, time-varying delays, and quantization errors in the distributed radar. Finally, the effectiveness of the proposed method is validated through the simulation example.

Enhancing security control in Markov jump networked systems against DoS attacks: A dynamic-memory based event-triggered mechanism

This study addresses the dynamic-memory-based event-triggered H∞ control problem for Markov jump networked systems under denial-of-service attacks. By utilizing a unified approach, the characteristics of denial-of-service attacks are comprehensively captured and incorporate constraints on attack duration. Striking a balance between system performance and triggering frequency, we propose an enhanced dynamic-memory-based event-triggered mechanism. The incorporation of multiple Lyapunov functions establishes robust constraints, ensuring asymptotic mean-square stability and H∞ noise attenuation performance for closed-loop Markov jump networked systems. Simulation results using an unmanned aerial vehicle model show that the proposed controller is effective against denial-of-service attacks, and the performance is significantly improved compared to the other two research results.

Event-Based Two-Step Transmission Mechanism for the Stabilization of Networked T-S Fuzzy Systems With Random Uncertainties.

This article studies an event-based two-step transmission mechanism (TSTM) in the control design for networked T-S fuzzy systems. The transmission task is achieved in two steps. Consecutive triggering packets are relabeled in the first step by applying a traditional event-triggered mechanism (ETM). Then a probabilistic approach is employed to determine which packet is a real release packet (RRP) in the second step. This event-based TSTM is particularly suitable for scenarios in which traditional ETMs are unable to determine which packets are redundant. By discarding most of the unnecessary data packets, especially when the system is tending toward stability, the burden on the network bandwidth is reduced. To establish a control strategy for T-S fuzzy-based nonlinear systems with random uncertainties, a new timing analysis technique is proposed. Additionally, the necessary conditions for a nonlinear system's mean-square asymptotic stability (MSAS) are derived. Finally, two practical applications demonstrate the effectiveness of the suggested transmission mechanism in networked T-S fuzzy systems.

Disturbance rejection-based non-fragile hybrid-triggered control design for repeated scalar nonlinear systems

This article features the composite disturbance estimation and non-fragile hybrid-triggered control problems for continuous-time repeated scalar nonlinear systems prone to external disturbances. Priorly, the proportional integral observer comprising of both proportional and integral loops is incorporated to obtain better state estimations. Further, the external disturbance weakening the system performance is carefully estimated by deploying an improved equivalent-input-disturbance technique. Then, the availed disturbance estimate is blended into the control algorithm to exterminate the influence of the disturbance acting upon the proffered system. Next, a hybrid-triggered control comprised of a transition among event and time triggered paradigms are considered to reduce the network transmittance and also to simultaneously enhances the system outcomes. On top of that, the perturbations in controller gain matrix are taken into concern in order to make the controller more resilient towards redundant changes. Following that, utilising the Lyapunov theory, we obtain the mean-square asymptotic stability requirements for the developed system with the use of linear matrix inequalities and configure the gain matrices. Successively, the credibility of the synthesised control system is portrayed by exhibiting two numerical examples.

Stabilization of Periodic Piecewise Time-Varying Systems With Time-Varying Delay Under Multiple Cyber Attacks: An Augmented Lyapunov Functional Approach.

This article investigates the asymptotic stabilization of periodic piecewise time-varying systems with time-varying delay under various cyber attacks, particularly deception and DoS attacks. The addressed system is reformed into a number of time-varying subsystems based on the time interval for each period. Following that, a state-feedback controller with periodic time-varying gain parameters is developed to solve the stabilization problem. The control design depicts the possibility of the aforementioned cyber attacks with two mutually exclusive stochastic Bernoulli distributed parameters. Then, an augmented Lyapunov-Krasovskii functional with periodically varying matrices is used to determine the conditions for designing the proposed controller that ensures the mean-square asymptotic stability of the addressed system. The results of numerical examples support the conclusion that the proposed method is effective and superior, regardless of the cyber attacks involved.

A memory state-feedback controller via random pocket dropouts for multi-agent systems with external disturbance

This study explores the challenge of achieving consensus in multi-agent systems (MASs) when facing the random packet dropouts and disturbances. It employs memory state-feedback control (MSFC) in the context of undirected graphs and specified leader agents. The analysis focuses on mean square consensus, considering MASs within strongly connected networks or networks with undirected spanning trees. The MSFC approach is developed to ensure asymptotic consensus despite packet dropouts and also to reduce the impact of disturbances. Specifically, the consensus analysis leverages the Lyapunov-Krasovskii functional (LKF) framework, and the necessary conditions for implementing the proposed MSFC are established using linear matrix inequalities (LMIs). The system, augmented with an H ∞ attenuation level is guaranteed to achieve asymptotic mean-square stability according to the provided criteria. In conclusion, two examples are provided to illustrate the effectiveness and practicality of the proposed control mechanism.

Asynchronous sampled-data dynamic output feedback control for Markovian jump neural networks via a double-mode-dependent Lyapunov functional

This paper discusses the asynchronous switching problem of Markovian jump neural networks (MJNNs) with mode-dependent time delays. Due to the factors such as communication induced phenomena or the incomplete availability of system modes, asynchronous switching between the system mode and the controller mode is a common phenomenon. Therefore considering the mode mismatch phenomenon and the incomplete measurement of system state, we propose an asynchronous dynamic output feedback control (DOFC) law. Unlike the traditional DOFC, the sampled-data strategy is introduced into DOFC to alleviate the burden of the communication network. In light of the sampled-data DOFC, an augmented dynamic system is modeled. To fully employ the mode information of asynchronous switching and to relax the conservativeness of the results, a double-mode-dependent Lyapunov functional is constructed, which depends both on the system modes and the DOFC modes. Then, a less conservative stability condition is obtained to guarantee mean-square asymptotic stability (MSAS) of the augmented system. On the basis of the stability condition, a design algorithm is attained to solve the gain matrices of the asynchronous DOFC. Finally, a simulation example is given to illustrate the validity and superiority of the developed results.

Disturbance attenuation for neutral Markovian jump systems with multiple delays

The work explores the study of a neutral Markovian jump system that contains multiple delays, external disturbances, and unknown non-linear uncertainties. To overcome the tracking problem, a modified repetitive controller infused with the higher equivalent-input-disturbance approach and the extended Smith predictor approach is suggested. To guarantee the mean-square asymptotic stability of the system, an appropriate mode-dependent loop-based Lyapunov–Krasovskii functional is used. The proposed controller explicitly forces the system output and accurately follows any supplied periodic reference signal. Subsequently, the efficiency of the recommended technique is demonstrated with the simulations that validate the outcomes by comparing them to the existing results.

Co-Design of Adaptive Event-Triggered Mechanism and Asynchronous H∞ Control for 2-D Markov Jump Systems via Genetic Algorithm.

This article concerns the co-design scheme of the adaptive event-triggered mechanism (AETM) and asynchronous H∞ control for two-dimensional (2-D) Markov jump systems. First, we introduce a hidden Markov model with the observation that the asynchronous phenomenon is inevitable between the plant mode and the controller mode. Besides, for economizing the communication times, an innovative 2-D AETM is constructed, which can dynamically regulate the event-triggered thresholds to strive for better system performance. Then, by utilizing the 2-D Lyapunov stability theory, nonlinear matrix inequalities are built to ensure the asymptotic mean-square stability with an H∞ performance for the closed-loop 2-D system. To avoid introducing any conservatism when handling the above nonlinear matrix inequalities, a binary-based genetic algorithm (BGA) is exploited to treat some variables as known, such that derive some directly solvable linear matrix inequalities. Finally, a simulation example is provided to verify the effectiveness of the proposed 2-D AETM-based asynchronous controller strategy with a BGA.

Stabilization of DFIG-based wind turbine with active and reactive power: A coupling memory state-feedback control scheme

In this paper, we examine a stabilization problem for the active and reactive power of doubly fed induction generator (DFIG)-based wind turbine (WT) through fuzzy coupling memory state-feedback control (CMSFC). In order to narrate the nonlinear terms in the proposed system, a more efficacious Takagi–Sugeno (T-S) fuzzy theory is utilized. The effective T-S fuzzy model describes the behavior of the nonlinear model into linear sub-models based on IF-THEN fuzzy membership functions and the corresponding fuzzy CMSFC is proposed. The main intention of this paper is to stabilize the active and reactive power constant, control the stator and rotor voltages of α−β frames when enhancing the system stable output power. To do this, a fuzzy CMSFC strategy is designed. By constructing a Lyapunov-Krasovskii functional (LKFs) with the effect of constant time-delay, the delay-dependent sufficient criteria are derived in the form of linear matrix inequalities (LMIs), which can be easily assessed by MATLAB LMI Control toolbox. Based on the delay-dependent sufficient criteria, the mean-square asymptotic stability of the DFIG-based WT system under the proposed controller is also achieved. Finally, we demonstrate the feasibility and efficacy of the proposed method through numerical simulations and comparative results.

Event-triggered-based [formula omitted] control for Markov jump cyber-physical systems against denial-of-service attacks

This paper is concerned with the event-triggered-based H∞ control problem for Markov jump cyber-physical systems against denial-of-service attacks. The uniform upper and lower bounds are used to describe the characteristics of aperiodic denial-of-service attacks. An event-triggered scheme is introduced to reduce the waste of resources and avoid communication channel congestion. Based on multi-Lyapunov functions, sufficient conditions are proposed to guarantee the asymptotic mean-square stability and H∞ performance of the switched closed-loop Markov jump cyber-physical systems. By solving linear matrix inequalities, the event-triggered-based controller gain matrices, and H∞ performance index are obtained. In the simulation, an F-404 aircraft engine system is employed to clarify the validity of the proposed event-triggered-based controller design approach in face of denial-of-service attacks.

Hybrid-triggered and fault-tolerant observer-based control for neural networks under malicious attacks

Based upon hybrid-triggered mechanism, this article inspects fault-tolerant issue based (Q,S,R) dissipative control for neural networks system along with malcious attacks and external disturbances. To be precious, conventional Luenberger observer is employed to estimate the system state and malicious attack signal, whereas the presence of smoothed signal of malicious attack in the system state will not allow the augmented state to be precisely estimate. Moreover, the hybrid-triggered mechanism which incorporates both time- and event-triggered scheme is initiated to mitigate the redundancy of network transmission and secures the network resources. Preciously, the stochastic switching within the mechanism satisfies the Bernoulli distribution. The main intention of this study is to develop a hybrid-triggered scheme and a fault-tolerant controller for ensuring the mean-square asymptotic stability for the desired neural networks with (Q,S,R) dissipative performance index. Assisted by Lyapunov stability theory and some inequality techniques, an adequate criterion has been attained in the configuration of linear matrix inequalities (LMIs) to guarantee the asymptotic stability of the neural networks system. Further, the anticipated gain matrices are attained with the strength of obtained LMIs. In the final analysis, the applicability and efficacity of the proposed control model are reflected through two numerical examples.

Event-Triggered and Self-Triggered L∞ Control for Markov Jump Stochastic Nonlinear Systems Under DoS Attacks.

This article investigates event-triggered and self-triggered L∞ control problems for the Markov jump stochastic nonlinear systems subject to denial-of-service (DoS) attacks. When attacks prevent system devices from obtaining valid information over networks, a new switched model with unstable subsystems is constructed to characterize the effect of DoS attacks. On the basis of the switched model, a multiple Lyapunov function method is utilized and a set of sufficient conditions incorporating the event-triggering scheme (ETS) and restriction of DoS attacks are provided to preserve L∞ performance. In particular, considering that ETS based on mathematical expectation is difficult to be implemented on a practical platform, a self-triggering scheme (STS) without mathematical expectation is presented. Meanwhile, to avoid the Zeno behavior resulted from general exogenous disturbance, a positive lower bound is fixed in STS in advance. In addition, the exponent parameters are designed in STS to reduce triggering frequency. Based on the STS, the mean-square asymptotical stability and almost sure exponential stability are both discussed when the system is in the absence of exogenous disturbance. Finally, two examples are given to substantiate the effectiveness of the proposed method.

Balanced implicit methods with strong order 1.5 for solving stochastic differential equations

The aim of this article is to propose a family of balanced implicit methods and split-step balanced implicit methods for solving Itô stochastic differential equations. These numerical methods represent a class of highly efficient linear-implicit schemes which covered the implicitness in the stochastic terms. The convergence in mean-square with strong order 1.5 and the asymptotic mean-square stability properties of these methods are analysed. What is more, the linear mean-square stability regions of some proposed methods are given. Several numerical examples are carried out to illustrate the theoretic findings.

Asymptotical Stability and Exponential Stability in Mean Square of Impulsive Stochastic Time-Varying Neural Network

The effect of impulse on stability of neural network is evident not only in performance, that is, impulsive control and impulsive interference. The amount of impulse has a certain impact on stability of neural network. Unlike traditional average impulsive interval, a new strategy is applied in this paper, namely, impulsive density. Based on this strategy, by constructing Lyapunov function, we establish sufficient conditions for mean square asymptotical stability of impulsive stochastic time-varying neural network without time delay. As well as, under this strategy and uniformly asymptotically stable function, by combining trajectory based approach and improved Razumikhin method, mean square exponential stability criterion of impulsive stochastic time-varying neural network with time delay is established. Finally, to demonstrate the viability of our theoretical findings, some instances are provided.

Construction of mean-square Lyapunov-basins for random ordinary differential equations

<p style='text-indent:20px;'>We propose a straightforward basin search algorithm to determine a suitably large level set of the mean-square Lyapunov-function that corresponds to the linearization about an path-wise equilibrium solution of a random ordinary differential equation (RODE). Noise intensity plays a crucial role for how similar the behavior of solutions of RODEs is compared to the corresponding deterministic system. In this regards, the basin search algorithm also allows to numerically estimate up to which noise intensities linearized mean-square asymptotic stability remains.</p>

Adaptive Memory-Based Event-Triggered Fault Detection for Networked Stochastic Systems

This brief concerns the event-triggered fault detection problem for a class of networked nonlinear stochastic systems with randomly occurring dropouts and time-varying delays to guarantee the safety and reliability of systems. In order to save limited communication bandwidth, a novel adaptive memory-based event-triggered scheme (ETS) is developed, based on which a memory-based fault detection filter (FDF) is constructed to generate residual signal. Then, an event-triggered fault detection framework is established, which is mainly composed of stochastic system, ETS, FDF, fault weighting, and residual evaluation. With considering the ETS, random dropouts, and time-varying transmission delays, the criterion of mean-square asymptotic stability and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> performance is given such that the residual signal is sensitive to faults while robust against disturbance. Then, the co-design method of memory-based ETS and FDF is proposed. Finally, a simulation case is provided to demonstrate the effectiveness and advantages of the proposed method.

Security Enhancement for Longitudinal Vehicle Platooning Under Denial-of-Service Attacks: From Resilient Controller Design Perspective

Longitudinal vehicle platooning provides one of the critical ancillary services in autonomous intelligent transportations for maintaining the appropriate longitudinal distance with preceding vehicles. In view of the vulnerabilities of control module to underlying denial-of-service (DoS) attacks, this paper designs a resilient controller for longitudinal vehicle platooning to realize security enhancement. Firstly, the DoS attacks on communication links from sensors to controllers are depicted by random Bernoulli variables. Then, robust mean-square asymptotic stability criteria are derived for the composite system model, based on which the resilient controller gains are obtained. Finally, simulation results validate the effectiveness of the presented resilient controller under different DoS attack probabilities.

The stability of a stochastic discrete SIVS epidemic model with general nonlinear incidence

In this paper, based on Euler–Marryama method and theory of stochastic processes, a stochastic discrete SIVS epidemic model with general nonlinear incidence and vaccination is proposed by adding random perturbation and then discretizing the corresponding stochastic differential equation model. Firstly, the basic properties of continuous and discrete deterministic SIVS epidemic models are obtained. Then a criterion on the asymptotic mean-square stability of zero solution for a general linear stochastic difference system is established. As the applications of this criterion, the sufficient conditions on the stability in probability of the disease-free and endemic equilibria for the stochastic discrete SIVS epidemic model are obtained. The numerical simulations are given to illustrate the theoretical results.

Convergence and Stability of a Split-Step Exponential Scheme Based on the Milstein Methods

We introduce two approaches by modifying split-step exponential schemes to study stochastic differential equations. Under the Lipschitz condition and linear-growth bounds, it is shown that our explicit schemes converge to the solution of the corresponding stochastic differential equations with the order 1.0 in the mean-square sense. The mean-square stability of our methods is investigated through some linear stochastic test systems. Additionally, asymptotic mean-square stability is analyzed for the two-dimensional system with symmetric and asymmetric coefficients and driven by two commutative noise terms. In particular, we prove that our methods are mean-square stable for any step-size. Finally, some numerical experiments are carried out to confirm the theoretical results.