Lyapunov Function Approach Research Articles

Observer-Based Distributed Event-Triggered Secure Consensus of Multi-Agent System With DoS Attack

This paper addresses the distributed secure consensus problem for linear multi-agent systems (MAS) with unmeasurable states and Denial-of-Service (DoS) attacks. The observer is designed to be used in estimating unmeasurable states of agents. Then, an observer-based distributed event-triggered control protocol is proposed to save network resources. By using the piecewise Lyapunov function approach, several sufficient conditions for ensuring secure consensus are obtained. Further, a rigorous theoretical analysis shows that the given event-triggering scheme exhibits no Zeno behavior. Finally, the effectiveness of the proposed method is verified by numerical simulation.

Resilient Load Frequency Control of Islanded AC Microgrids Under Concurrent False Data Injection and Denial-of-Service Attacks

Due to malicious cyber attacks, the frequency regulation of an islanded microgrid (MG) with load changes and wind/solar power fluctuations may not be guaranteed and the overall system may even be destabilized. The MG frequency control thus faces new challenges. In response to these challenges, this paper addresses a resilient load frequency control (LFC) problem for islanded AC-MGs under simultaneous false data injection (FDI) attacks and denial-of-service (DoS) attacks. Toward this aim, a new piecewise observer is constructed to provide the real-time estimates of the unavailable system state and the unknown FDI attack signal. Furthermore, a resilient <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {H}_{\infty }$ </tex-math></inline-formula> LFC scheme is developed to suppress the attack impacts. The novelty of this study lies in the development of an attack-parameter-dependent time-varying Lyapunov function approach to achieve stability analysis and resilient observer/controller design against concurrent FDI attacks and intermittent DoS attacks. Specifically, a tractable observer design criterion is first derived such that the estimation error is exponentially stable under a specified <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {H}_{\infty }$ </tex-math></inline-formula> performance level. Then a design criterion on the existence of the resilient controller is presented to guarantee the exponential stability of the resulting closed-loop system in the presence of the attacks, while preserving the anticipated <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {H}_{\infty }$ </tex-math></inline-formula> performance level. Finally, comparative simulation studies in various attack scenarios and different parameter settings are presented to verify the efficiency of the obtained theoretical results.

Asymptotic stability for a class of switched stochastic delayed differential systems

AbstractSeveral novel th moment asymptotic stability criteria are established for switched stochastic delayed differential systems (SSDDSs) under the framework that the time‐delay is unbounded. These criteria are obtained by constructing some special sets and using the Lyapunov function approach. The features of the criteria show that the form of the unbounded delay plays an important role in keeping the stability of the related systems. As a corollary, if the number of subsystems is only one, the system is reduced to stochastic delayed differential systems (SDDSs), and the criterion of the th moment asymptotic stability for this system is also obtained, which can improve the existing results for SDDSs with unbounded delays. Finally, two numerical examples are given to show the significance of our results.

Output-feedback control for discrete-time switched systems via non-monotonic switched Lyapunov function approach

This paper investigates the output-feedback control for discrete-time switched linear systems. By extending the methodology of switched Lyapunov functions (SLF), a non-monotonic SLF approach is proposed to analyse the stability of the resulting closed-loop system under arbitrary switching. This approach relaxes the requirement of monotonicity to conventional SLF approach, and hence it will lead to less conservative results. First, the stability of discrete-time switched systems is analysed, and then an output-feedback controller design method is proposed based on the obtained stability results. The controller design problem is formulated in term of LMIs, and relaxed variables are introduced in the synthesis conditions to improve the design freedom. Finally, three examples are used to verify the effectiveness and application potential of the proposed methods.

Asymptotic analysis of SIR epidemic model with nonlocal diffusion and generalized nonlinear incidence functional

We aim in this research to determine the global stability of equilibrium states for an SIR epidemic model with nonlocal diffusion and nonlinear incidence function in a heterogeneous environment. For achieving this result, we consider that the model parameters are Lipschitz continuous functions. At the infection free‐equilibrium, the eigenvalue problem has a principal simple eigenvalue corresponding to strictly positive eigenfunction which is expressed as . By a Lyapunov function approach, we show the global stability of drug‐free equilibrium for . For , and using persistence theory for dynamical systems, we show that the epidemic will persist and the unique endemic equilibrium state is globally stable by constructing a proper Lyapunov function.

Quasisynchronization of Reaction–Diffusion Neural Networks Under Deception Attacks

This study focuses on the quasisynchronization problem for reaction–diffusion neural networks (RDNNs) in the presence of deception attacks. Under deception attacks, a time–space sampled-data (TSSD) control mechanism is proposed for RDNNs. Compared with traditional control strategies, the proposed control mechanism can not only save network bandwidth but also improve the cybersecurity of communications. Inspired by Halanay’s inequality, a new inequality is proposed, which can be effectively applied to the quasisynchronization problem for dynamical systems. Then, by using this inequality and the Lyapunov functional approach, quasisynchronization criteria are set for RDNNs. The desired control gain is gained from solving a group of linear matrix inequalities. Moreover, in the absence of deception attacks, the exponential synchronization problem is studied for RDNNs. In the end, simulation results are given to demonstrate the usefulness of the theoretical analysis.

Prescribed Finite-Time Adaptive Neural Tracking Control for Nonlinear State-Constrained Systems: Barrier Function Approach.

The purpose of this article is to present a novel backstepping-based adaptive neural tracking control design procedure for nonlinear systems with time-varying state constraints. The designed adaptive neural tracking controller is expected to have the following characters: under its action: 1) the designed virtual control signals meet the constraints on the corresponding virtual control states in order to realize the backstepping design ideal and 2) the output tracking error tends to a sufficiently small neighborhood of the origin with the prescribed finite time and accuracy level. By combining the barrier Lyapunov function approach with the adaptive neural backstepping technique, a novel adaptive neural tracking controller is proposed. It is shown that the constructed controller makes sure that the output tracking error converges to a small neighborhood of the origin with the prespecified tracking accuracy and settling time. Finally, the proposed control scheme is further tested by simulation examples.

Passivity-Based Output Consensus for Second-Order Nonlinear Multiagent Systems

The output consensus for a second-order nonlinear multiagent system (MAS) with mismatched input and output vectors is investigated by exploiting the output strict passivity (OSP). By resorting to the Lyapunov functional approach and the state feedback control method, an OSP criterion for the MAS is derived. Based on the OSP and the relationship between output consensus and the OSP, a sufficient condition to ensure the output consensus of the MAS is obtained. At last, a numerical simulation is given to substantiate the merits of the obtained theoretical results.

Cooperative Output Regulation of T–S Fuzzy Multiagent Systems Under Switching Directed Topologies and Event-Triggered Communication

In this article, the event-triggered cooperative output regulation problem of T–S fuzzy multiagent systems under jointly connected switching directed topologies is investigated. A distributed sampled-data event-triggered scheme is proposed such that the estimator, which estimates the exosystem, transmits the data information to its neighbors under the switching directed topologies at its triggering instants. The continuous event detection and triggering Zeno behavior are avoided via aperiodic sampling. Then, the time-dependent Lyapunov functional approach together with the dwell time technique is utilized, such that the estimation errors converge to zero exponentially. Furthermore, the observer-based fuzzy controllers are developed to ensure the solvability of the cooperative output regulation. Besides, the advantage of the distributed sampled-data event-triggered scheme is that the data transmissions caused by triggerings and switchings are autocephalous, which avoids the situation that triggering must occur at the switching points. Finally, an example is given to show the validity of results.

Backstepping-Based Controller Design for Uncertain Switched High-Order Nonlinear Systems via PI Compensation

This article presents an effective method to address the tracking control problem arising in uncertain switched high-order nonlinear system in strict-feedback form. The system under consideration contains unknown functions, which causally make the asymptotic tracking performance difficult to be achieved. By adopting the adding a power integrator approach in the framework of backstepping, a novel tracking controller is developed to guarantee an asymptotic tracking performance in the presence of the approximation error cased by neural networks (NNs) under arbitrary switching. The main contributions lie in: 1) the article for the first time embeds the backstepping technique in designing a kind of discontinuous controller with proportional integral (PI) compensation and 2) with the help of Filippov’s theory, a new defined system described by differential inclusions can be first obtained by taking some transformations, and then a novel nonsmooth Lyapunov function approach along with its upper right Dini derivative technique is applied to complete the construction of the discontinuous controller. Finally, two simulation examples are exhibited to verify the validity of the proposed design techniques.

Global dynamics of a diffusive SEICR HCV model with nonlinear incidences

To capture the transmission dynamics of hepatitis C virus, we propose and study a reaction–diffusion nonlinear SEICR model, which includes latent, acute, and chronic infection stages. We first establish the well-posedness and boundedness of the model. It is shown the disease-free steady state is globally asymptotically stable if the basic reproduction number R0<1 while the model is uniformly persistent if R0>1. For the special case where the model parameters are spatially homogeneous, we not only derive the explicit expression of R0 but also show that the positive steady state is globally asymptotically stable if R0>1 through the approach of Lyapunov functionals. The feasibility of the theoretical results is demonstrated by numerical simulations. Moreover, we carry out the sensitivity analysis of R0 with respect to the parameters and thus the important parameters significantly influencing the dynamic behaviors are identified.

Polynomial synchronization of complex-valued inertial neural networks with multi-proportional delays

This paper investigates the polynomial synchronization (PS) problem of complex-valued inertial neural networks with multi-proportional delays. It is analyzed based on the non-separation method. Firstly, an exponential transformation is applied and an appropriate controller is designed. Then, a new sufficient criterion for PS of the considered system is derived by the Lyapunov function approach and some inequalities techniques. In the end, a numerical example is given to illustrate the effectiveness of the obtained result.

Sampled-Data-Based Dissipative Stabilization of IT-2 TSFSs Via Fuzzy Adaptive Event-Triggered Protocol.

In this research, the fuzzy adaptive event-triggered control (FAETC) issue is addressed for uncertain nonlinear networked control systems with network-induced delays (NIDs) and external disturbance. In order to effectively capture parameter uncertainties, the interval type-2 (IT-2) Takagi-Sugeno (T-S) fuzzy model is utilized to represent such a system. Considering the fact that the controller is fuzzy and the threshold can promptly update its state according to the current and latest sampled signals (SSs), it becomes quite challenging to solve the dissipative stabilization problem (DSP) with the existing schemes. Then, a novel FAETC protocol is put forward to reduce the utilization of communication resources while maintaining the desired control performance. By employing the fuzzy-logic technique and the looped Lyapunov functional (LLF) approach, sufficient conditions related to the relationship between the stabilization and desired dissipative performance for the resulting system are formulated. A numerical example is used to validate the feasibility of our attained results.

Sampled-Data Asynchronous Control for Switched Nonlinear Systems With Relaxed Switching Rules.

This article investigates the problem of quantized sampled-data control for continuous-time switched Takagi-Sugeno (T-S) fuzzy systems with the asynchronous phenomenon. First, considering that the system and controller modes could not be perfectly synchronized all the time, we study possible cases of mode mismatching by exploiting the average dwell time (ADT) switching strategy. Since the fact that a minimum dwell time of each subsystem is not required in the ADT switching rule, multiple system switching is allowed within one sampling interval, which overcomes the limitation of at most once switching during any sampling interval in existing works. Second, the asynchronous premise variables between the fuzzy system and fuzzy controller are taken into consideration in the quantized sampled-data control scheme. Then, by virtue of the Lyapunov function approach, we obtain sufficient conditions to guarantee that the asynchronously switched T-S fuzzy system is exponentially stable with quantized sampled-data input. Furthermore, the weighted L2 -gain is discussed for the system under external disturbance, and an H∞ state feedback controller is correspondingly designed with prescribed disturbance attenuation. Finally, the validity and advantage of the proposed methods are illustrated by two examples.

Finite-/Fixed-Time Stability of Nonautonomous Functional Differential Inclusion: Lyapunov Approach Involving Indefinite Derivative.

This article investigates a type of nonautonomous delayed differential equation (DDE) with discontinuity. Under the framework of the Filippov state solution, the finite-time stability (FNTS)/fixed-time stability (FXTS) problems of nonautonomous functional differential inclusion (FDI) are studied via the generalized Lyapunov functional method. The generalized Lyapunov functional used in this article is allowed to obtain an indefinite time derivative almost anywhere (a.a.) along the system's state solutions. Nevertheless, the classic Lyapunov functional requires that its time derivative retains seminegative/negative definiteness anywhere. As a result, novel FNTS and FXTS criteria of the trivial state solution for FDI are established. Moreover, the settling time (ST) of FNTS/FXTS is provided. Then, the developed Lyapunov functional approach is applied to realize the finite-/fixed-time stabilization control of delayed neuron networks (DNNs) possessing discontinuous activation and ball motion models. The proposed method and results concerning FNTS/FXTS are of great significance in neural network (NN)/mechanical control engineering applications.

Quantized [formula omitted] filtering for networked persistent dwell-time switched piecewise-affine systems

In this study, the problem of quantized H∞ filtering is addressed for networked switched piecewise-affine systems, in which the switching mechanism obeys the persistent dwell-time constraint. To process the measurement output and schedule the transmission sequence for alleviating the burden of the limited communication channel, a logarithmic quantizer is employed, which can further improve the bandwidth utilization in networked switched systems. On the basis of state-space division, the objective is to design a mode-dependent and region-dependent filter that ensuresthe filtering error system is globally uniformly exponentially stable and meets an H∞ performance. By using the mode-dependent Lyapunov function approach and employing appropriate decoupling methods, sufficient conditions for obtaining desired filter gains are deduced. Eventually, two illustrated examples are given to demonstrate the effectiveness of our proposed method.

General stabilization of non-autonomous hybrid systems with delays and random noises via delayed feedback control

The feedback control, derived from delayed state observations, was triumphantly imported to H∞ and exponentially stabilize an unstable nonlinear hybrid system with time-invariant delay and random noise, which is adapt to autonomous systems. Spontaneously, given an unstable non-autonomous hybrid system with time-dependent delay and random noise, can one import a feedback control, derived from delayed state and mode observations, to stabilize it? Fortunately, this will be well done by the approach of multiple Lyapunov functionals. Surprisingly, it is revealed that the stabilization can be achieved not only in the forms of H∞ stability and exponential speed but also of polynomial speed and general speed. Furthermore, the interesting result with respect to polynomial growth at most is as well yielded here.

Exponential Stability of Switched Neural Networks with Partial State Reset and Time-Varying Delays

This paper mainly investigates the exponential stability of switched neural networks (SNNs) with partial state reset and time-varying delays, in which partial state reset means that only a fraction of the states can be reset at each switching instant. Moreover, both stable and unstable subsystems are also taken into account and therefore, switched systems under consideration can take several switched systems as special cases. The comparison principle, the Halanay-like inequality, and the time-dependent switched Lyapunov function approach are used to obtain sufficient conditions to ensure that the considered SNNs with delays and partial state reset are exponentially stable. Numerical examples are provided to demonstrate the reliability of the developed results.

Finite-time H∞ control of discrete-time switched systems based on transferring-dependent Lyapunov function approach

This paper studies the finite-time issues (finite-time stability, finite-time boundedness, finite-time [Formula: see text] control) of discrete-time switched systems. Different from the existing Lyapunov function (LF) approaches only concerning activated subsystem, a novel approach for constructing LF is first proposed, which not only depends on the subsystem the switching reaches but also is closely related to the freshly inactive subsystem. Based on this, a transferring-dependent convex Lyapunov function (CLF) and a transferring-dependent LF are introduced, under which the improved finite-time stability results are deduced with admissible edge-dependent average dwell time (AED-ADT) technique. In light of the merits of established finite-time stability criteria, two transferring-dependent controllers are devised—that is, transferring-dependent convex controller (TD-CC) and transferring-dependent ordinary controller (TD-OC)—to perform finite-time control synthesis. Then, the finite-time [Formula: see text] control is further investigated based on the obtained control synthesis results. The designed transferring–dependent controllers can guarantee that the underlying system is finite-time bounded (FTB) with a prescribed [Formula: see text] performance under tighter AED-ADT switching signals. Besides, it is the first time to use the multiple convex Lyapunov function (MCLF) to investigate the finite-time issues. Finally, two numerical examples and a practical example are used to verify the effectiveness of the developed results.

A New Adaptive Controller for Linear Systems: A Model Reference Approach

In this paper, a finite-time model reference adaptive controller is proposed to solve the tracking problem for a class of linear time-invariant systems with parameter uncertainties. The convergence to zero in a finite time for the tracking and parameter identification errors is ensured. The convergence proofs are developed based on Lyapunov function approach. Finally, some simulation results show the feasibility of the proposed approach.