Finite-time Mean Square Research Articles

Hybrid-driven based reliable control for uncertain semi-Markov jump cyber–physical systems via two-sided looped-functional

In this paper, the problem of input–output finite-time mean square stabilisation for semi-Markov jump cyber–physical systems is addressed under the frame of generally uncertain transition rates through the hybrid-triggering-based reliable control technique. And, the undertaken system is susceptible to several vulnerable elements such as linear fractional uncertainty, actuator faults, deception attacks and external disturbances. Moreover, a hybrid-triggered approach that fuses the both time-triggered and event-triggered strategies is implemented for the addressed system which significantly reduces the number of unimportant communication transmissions inside the network. Subsequently, a reliable control law is configured by utilising the established hybrid-trigger mechanism and taking into account the actuator fault. In addition, the deception attacks and hybrid-trigger mechanism are characterised by the stochastic variables that adhere to the Bernoulli distribution. Furthermore, by framing a mode-dependent two-side looped Lyapunov–Krasovskii functional and deploying the advanced integral inequalities, adequate criteria are developed within the context of linear matrix inequalities which ensures that the desired result. After that, the controller gain values is determined based on the inferred appropriate criteria. Ultimately, the simulation results, including the RLC circuit series, are shown in order to verify the suitability and potential of the demonstrated findings.

Finite-time stability for impulsive stochastic nonlinear system with uncertain parameter

This paper considered the finite-time mean square stability for impulsive stochastic nonlinear system(ISNS) with uncertain parameter. By selecting the modal dependent Lyapunov functional, using average impulsive interval approach and combining Linear Matrix Inequality (LMI) method, the correlation stability criterion of ISNS was obtained. A gain matrix of the feedback controller is obtained on the basis of this sufficient condition. Finally, the LMI toolbox in Matlab was used for data simulation, and the relevant state trajectory demonstrates the availability of the proposed theory.

Quantized fault-tolerant pinning control for finite-time H∞ synchronization of T-S fuzzy discrete Markovian-jump complex networks subject to heterogeneous delays

This paper investigates the finite-time pinning synchronization problem for a class of T-S fuzzy discrete Markovian-jump complex networks (TSFDMCNs) influenced by heterogeneous delays. The evolution of system parameters follows the Markov jump process according to a transition probability matrix with partly unknown elements. Based on the system state output, quantized fault-tolerant pinning controller (QFTPC) is designed to overcome communication limitations and varying actuator fault. Besides, the asynchronous signal generated by the hidden Markov model is employed in controller to make full use of received information. A novel mode-dependent Lyapunov- Krasovskii functional (LKF) is established to guarantee the error system mean-square finite-time bounded with the prescribed performance. In order to reduce conservatism of derived results, an improved Wirtinger-based inequality technique is applied in considering both lower and upper bounds of different delay. Finally, simulation examples illustrate the effectiveness and meliority of the proposed theoretical methods.

Mean-square finite-time synchronization of stochastic competitive neural networks with infinite time-varying delays and reaction–diffusion terms

This paper focuses on the mean-square finite-time synchronization (MFTS) of stochastic competitive neural networks with infinite time-varying discrete delays and reaction–diffusion terms (IRSCNNs). Different from other articles, this paper presents a new approach, which does not use finite-time stability theorem but uses integral inequality, Gronwall-type inequality and comparison strategy to study MFTS. In addition, two control schemes are designed: a feedback control scheme and a new adaptive control strategy, which can achieve MFTS of IRSCNNs. Finally, the correctness of the results is verified by examples.

Finite-time ℋ∞ filtering for Markov jump systems with uniform quantization

This paper is concerned with finite-time ℋ ∞ filtering for Markov jump systems with uniform quantization. The objective is to design quantized mode-dependent filters to ensure that the filtering error system is not only mean-square finite-time bounded but also has a prescribed finite-time ℋ ∞ performance. First, the case where the switching modes of the filter align with those of the MJS is considered. A numerically tractable filter design approach is proposed utilizing a mode-dependent Lyapunov function, Schur’s complement, and Dynkin’s formula. Then, the study is extended to a scenario where the switching modes of the filter can differ from those of the MJS. To address this situation, a mode-mismatched filter design approach is developed by leveraging a hidden Markov model to describe the asynchronous mode switching and the double expectation formula. Finally, a spring system model subject to a Markov chain is employed to validate the effectiveness of the quantized filter design approaches.

Multiple interval delay-dependent finite-time control of fuzzy stochastic systems

This work is concerned with multiple interval delay-dependent stochastic finite-time boundedness as well as input-output finite-time mean square stabilization for fuzzy plants against state constraints as well as input constraints. Nonlinear dynamics, intermittent actuator faults, exogenous disturbances, model uncertainties and intermittent sensor faults appear in the multiplicative form in these systems. The switching between the faulty and healthy conditions is described via semi-Markov chain. First, a semi-Markovian fault-tolerant controller is researched. Next, the closed-loop model is gathered. The issue of robust stochastic finite-time boundedness as well as input-output finite-time mean square stabilization against H∞ performance is realized via fuzzy stochastic Lyapunov function. Meanwhile, sufficient conditions are presented with linear matrix inequalities. At last, this validity of this approach in this paper is proved by two examples.

Event-Triggered Quantized Input-Output Finite-Time Synchronization of Markovian Neural Networks

This paper addresses the event-triggered input-output finite-time mean square synchronization for uncertain Markovian jump neural networks with partly unknown transition rates and quantization. Considering the limited network resources, an event-triggered technique and a logarithmic quantizer are both provided. The error system model with uncertainty is established in the unified framework. Then, based on Lyapunov functional approach, interesting results are presented to guarantee the properties of the input-output finite-time mean square synchronization for the error systems. Furthermore, some solvability conditions are induced for the desired input-output finite-time mean square synchronization controller under linear matrix inequality techniques. Eventually, the theoretical finding’s efficiency is shown by an example.

Resilient finite-time distributed event-triggered consensus of multi-agent systems with multiple cyber-attacks

This study addresses the resilient finite-time distributed event-triggered (ET) consensus control of multi-agent systems (MASs) with multiple cyber-attacks, such as replay, deception, and denial-of-service (DoS) attacks. For the first attempt, a model is proposed for multiple cyber-attacks on MASs under DoS, deception, and replay attacks, that occur stochastically in a unified framework. Furthermore, an appropriate distributed ET consensus control mechanism is proposed to handle the unwanted traffic in the network communication channel. This scheme determines whether or not the signal can be transmitted to each agent in MASs. Sufficient conditions for the consensus of MASs are derived using Lyapunov stability theory and linear matrix inequalities (LMIs), which ensure the exponentially mean-square finite-time stability. On the basis of the obtained conditions, the explicit expressions of the consensus control gain matrix and trigger parameter matrices are given. Eventually, simulation results are provided to verify the proposed theoretical results.

Quantitative Mean Square Exponential Stability and Stabilization of Linear Itô Stochastic Markovian Jump Systems Driven by Both Brownian and Poisson Noises

In this paper, quantitative mean square exponential stability and stabilization of Itô-type linear stochastic Markovian jump systems with Brownian and Poisson noises are investigated. First, the definition of quantitative mean square exponential stability, which takes into account the transient and steady behaviors of the system, is presented. Second, the relationship between general finite-time mean square stability, finite-time stochastic stability, and quantitative mean square exponential stability is proposed. Subsequently, some sufficient conditions for the existence of state feedback and observer-based controllers are derived, and an algorithm is offered to solve the matrix inequalities resulting from quantitative mean square exponential stabilization. Finally, the effectiveness of the proposed results is illustrated with the numerical example and the practical example.

Multiple delay-dependent event-triggered finite-time [formula omitted] filtering for uncertain networked random systems against state and input constraints

In this article, multiple delay-dependent event-triggered finite-time H∞ filtering as well as fault-tolerant control is discussed for networked random systems subject to state as well as input constraints. This is the first time to explore fault detection issue via filtering for networked random models. First, an event-triggered scheme is designed. Secondly, a zero order holder is studied. According to this event-triggered mechanism, a fault detection filter, a fault weighting system and a controller are investigated for the networked random system. And then an augmented system can be got. Sufficient conditions of mean-square finite-time boundedness with input-output finite-time mean square stabilization can be provided through the framework of linear matrix inequalities. Finally, these effectiveness and merits are verified by an example.

Dissipativity-Based Finite-Time Filtering for Uncertain Semi-Markovian Jump Random Systems With Multiple Time Delays and State Constraints

This article is concerned with the issue of dissipativity-based finite-time multiple delay-dependent filtering for uncertain semi-Markovian jump random nonlinear systems with state constraints. There are multiple time-varying delays, nonlinear functions, and intermittent faults (IFs) in the systems. This is one of the few attempts for the issue studied in this article. First, a filter is designed for the uncertain semi-Markovian jump random nonlinear systems. An augmented system with regard to the resulting filtering error is acquired. Then, sufficient conditions of the augmented system are generated by the stochastic Lyapunov function. Finite-time boundedness (FTB) and input-output finite-time mean square stabilization (IO-FTMSS) are both realized. The effectiveness and feasibility of the method are rendered via three examples.

Multiple Delay-Dependent Robust $H_\infty$ Finite-Time Filtering for Uncertain Itô Stochastic Takagi–Sugeno Fuzzy Semi-Markovian Jump Systems With State Constraints

This article investigates multiple delay-dependent robust <inline-formula><tex-math notation="LaTeX">$H_\infty$</tex-math></inline-formula> finite-time filtering for uncertain It&#x00F4; stochastic Takagi&#x2013;Sugeno (T&#x2013;S) fuzzy semi-Markovian jump systems with state constraints. Few studies exist for It&#x00F4; stochastic T&#x2013;S fuzzy semi-Markovian jump systems with state constraints. First, a T&#x2013;S fuzzy semi-Markovian jump filter is explored and a controller is designed. In terms of linear matrix inequalities, delay-dependent sufficient conditions as well as bounded real lemma are gathered by utilizing stochastic Lyapunov function. Robust finite-time boundedness and input&#x2013;output finite-time mean square stabilization are achieved and gain matrices of the filter and controller are obtained at the same time. A numerical example is presented to validate the feasibility of the proposed results in this article. And the admissible maximal delay bounds are calculated.

Multiple delay-dependent finite-time boundedness and input–output finite-time mean square stabilization of uncertain semi-Markovian jump systems with input constraint

This study is concerned with the problem of finite-time fault-tolerant control for uncertain semi-Markovian jump systems with input constraint and multiple time delays. There exist nonlinear functions, exogenous disturbances and measurement noise in these nonlinear systems. First, a dynamic output feedback controller is constructed for the uncertain semi-Markovian jump systems. A closed-loop system is earned. Next, sufficient stability conditions of the closed-loop system are obtained via stochastic Lyapunov function. Not only finite-time boundedness but also input-output finite-time mean square stabilization is achieved. This study is the first time to study. Finally, an example is provided to prove the novelty of the approach proposed in this paper.

Asynchronous Distributed Finite-Time H∞ Filtering in Sensor Networks With Hidden Markovian Switching and Two-Channel Stochastic Attack.

This article investigates the asynchronous distributed finite-time H∞ filtering problem for nonlinear Markov jump systems over sensor networks under stochastic attacks. The stochastic attacks, called two-channel deception attacks, exist not only between the Markov jump plant and the sensors but also among the sensors. It is assumed that the mode of the filter relies on, but is asynchronous with, that of the Markov jump plant. First, we establish a filtering error system that combines the Markov jump plant with the asynchronous filtering system. Then, we present an asynchronous distributed filter, which ensures the filtering error system mean-square finite-time bounded and satisfies a prescribed H∞ performance level under the two-channel attacks. Finally, an example is given to illustrate the effectiveness of the presented filter.

Adaptive Finite-Time Neural Control for a Class of Stochastic Nonlinear Systems With Known Hysteresis

This manuscript considers the finite time adaptive neural tracking control problem for a class of the nonstrict-feedback stochastic nonlinear systems with Bouc-Wen hysteresis input. During the design process, a Bouc-Wen model is first adopted to obtain the input hysteresis phenomenon. By fusion with the backstepping technique and the neural network approximation capability, the unknown nonlinearities are coped with, a constructive finite time adaptive neural network control strategy is proposed. Furthermore, the finite-time mean square stability of stochastic nonlinear systems is proved, and at last the effectiveness of the proposed control strategy is validated by the simulations.

Neural network-based finite-time control of quantized stochastic nonlinear systems

The finite-time tracking control of a class of stochastic quantized nonlinear systems is thought about in this article. Different from the studies on conventional finite-time control of stochastic systems, the quantized control problem is first taken into account and the nonlinear terms may be completely unknown. The quantization error and unknown nonlinearities make the existing finite-time stability criterion unavailable. By adopting the approximation ability of neural network, a novel adaptive neural control strategy is proposed, which removes the linear growth condition assumption for nonlinearities in existing finite-time studies. To be convenient for finite-time stability analysis of stochastic nonlinear systems, an important finite time stability criterion in integral form is first set up. Then, combining Jessen’s inequality and the proposed finite-time stability criterion, the finite-time mean square stability of stochastic nonlinear system is proved.

Finite-Time Fuzzy Control of Stochastic Nonlinear Systems.

This paper studies the finite-time stabilization of a class of stochastic nonlinear systems. Different from functions which are necessarily known in the conventional finite-time control of nonlinear systems, the nonlinear functions can be completely unknown in this paper. By applying fuzzy-logic systems to approximate the unknown nonlinearities, a novel adaptive finite-time control strategy is proposed. However, due to the existence of approximation errors, the existing finite-time stability criterion cannot be used to analyze the stability of stochastic nonlinear systems. To deal with this difficulty, a finite-time stability criterion, by utilizing the mean value theorem of integrals, is first established in Lemma 5, which plays a significant role in the finite-time stability analysis of stochastic nonlinear systems. Then, the finite-time mean square stability of a stochastic nonlinear system is proved by combining Lemma 3 with Jensen's inequality.

Input–output finite-time mean square stabilization of nonlinear semi-Markovian jump systems

This paper is concerned with the input–output finite-time mean square stabilization problem for a class of nonlinear semi-Markovian jump systems (SMJSs) with time-varying delay. Both time-varying factors of transition rates and states delay are considered to be bounded. Our main purpose is to derive some parameter-dependent sufficient criteria by designing a state feedback controller, to guarantee the input–output finite-time mean square stabilization for the underlying systems where the nonlinear term satisfies the conic sector constraint. Then, the stabilization conditions are obtained by employing a novel Lyapunov–Krasovskii functional, differential form Gronwall’s inequality, and an extra slack variable which is composed of the time-varying transition rates. Finally, a simulation example is provided to illustrate the effectiveness and merits of the proposed method.

Finite-Time Passivity of Stochastic Markov Jump Neural Networks with Random Distributed Delays and Sensor Nonlinearities

This paper investigates the problem of mean-square finite-time passivity of discrete-time stochastic Markov jump neural networks with distributed delays and sensor nonlinearities. The distributed delays and sensor nonlinearities are randomly varying and described by mode-dependent random sequences with known statistical information. The mean-square finite-time boundedness and mean-square finite-time passivity results are obtained based on Lyapunov-like functional method. And the mean-square finite-time passivity is also considered for neural networks with random infinite-distributed delays. Finally, a numerical example verifies the effectiveness of the method.

A Parameter-Dependent Sliding Mode Approach for Finite-Time Bounded Control of Uncertain Stochastic Systems With Randomly Varying Actuator Faults and Its Application to a Parallel Active Suspension System

This paper addresses the mean-square finite-time bounded control problem for uncertain stochastic systems via a sliding mode approach. The stochastic phenomena of randomly occurring uncertainties and randomly varying actuator faults modeled by two independent exponential distributions are addressed effectively. A key issue for the system under the consideration is how to ensure, for any prescribed finite (possibly short ) working time interval, the stochastic finite-time boundedness (SFTB) of the resultant closed-loop systems and the reachability of the specified sliding surface in mean-square sense. To this end, a parameter-dependent sliding mode control (SMC) law is designed to force ( with probability one ) the state trajectories into a domain around the specified sliding surface during the given finite-time interval. The upper bound of the sliding domain associated with the design parameters is obtained explicitly. The sufficient conditions are established, respectively, for guaranteeing the SFTB of the SMC systems over both reaching phase and sliding motion phase . Finally, the proposed finite-time SMC approach is illustrated via a parallel active suspension system.