lyapunov methods
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Author(s):  
Zhiwen Wang ◽  
Bin Zhang ◽  
Xiangnan Xu ◽  
Usman ◽  
Long Li

This paper investigates the security control problem of the cyber-physical system under false data injection attacks. A model predictive switching control strategy based on attack perception is proposed to compensate for the untrusted sequence of data caused by false data injection attacks. First, the binary attack detector is applied whether the system has suffered the attack. If the attack occurs, multistep correction is carried out for the future data according to the previous time data, and the waiting period [Formula: see text] is set. The input and output sequence of the controller is reconstructed, and the system is modeled as a constant time-delay switched system. Subsequently, the Lyapunov methods and average-dwell time are combined to provide sufficient conditions for the asymptotical stability of closed-loop switched system. Finally, the simulation of the networked first-order inverted pendulum model reveals that the control technique can efficiently suppress the influence of the attacks.


Author(s):  
Manjing Guo ◽  
Lin Hu ◽  
Lin-Fei Nie

Considering the impact of environmental white noise on the quantity and behavior of vector of disease, a stochastic differential model describing the transmission of Dengue fever between mosquitoes and humans, in this paper, is proposed. By using Lyapunov methods and Itô’s formula, we first prove the existence and uniqueness of a global positive solution for this model. Further, some sufficient conditions for the extinction and persistence in the mean of this stochastic model are obtained by using the techniques of a series of stochastic inequalities. In addition, we also discuss the existence of a unique stationary distribution which leads to the stochastic persistence of this disease. Finally, several numerical simulations are carried to illustrate the main results of this contribution.


2021 ◽  
Vol 18 (1) ◽  
pp. 172988142098674
Author(s):  
Zheping Yan ◽  
Da Xu ◽  
Tao Chen ◽  
Jiajia Zhou

Formation control is one of the essential problems in multi-unmanned underwater vehicle (UUV) coordination. In this article, a practically oriented UUV formation control structure and method are proposed for the problem of large communication in leader–follower approach. To solve the problem of large communication in multi-UUVs, local sensing means of acoustic positioning is used to provide the real relative distance and angle information for the follower UUV. So, only a small amount of state information of the leader UUV needs to be sent to the follower UUV by acoustic communication. Then, the formation control structure in absence of follower position information is proposed. In this control structure, only the relative distance and angle, as well as velocity and heading of the leader UUV, are used for the formation controller design of the follower UUV. Backstepping and Lyapunov methods are used to design the formation controller without position information of the follower UUV. Two formation configurations of rectangle and triangle with five UUVs are simulated to verify the effectiveness of the method proposed. The simulation results show that the follower UUV can successfully constitute and maintain the desired formation by controlling each real relative distance and angle.


2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Pierdomenico Pepe

<p style='text-indent:20px;'>A nonlinear version of Halanay's inequality is studied in this paper as a sufficient condition for the convergence of functions to the origin, uniformly with respect to bounded sets of initial values. The same result is provided in the case of forcing terms, for the uniform convergence to suitable neighborhoods of the origin. Related Lyapunov methods for the global uniform asymptotic stability and the input-to-state stability of systems described by retarded functional differential equations, with possibly nonconstant time delays, are provided. The relationship with the Razumikhin methodology is shown.</p>


2020 ◽  
pp. 177-188
Author(s):  
W. E. Fitzgibbon ◽  
J. J. Morgan ◽  
S. J. Waggoner

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Yang Liu ◽  
Weidong Li

The dynamic model of high-speed trains (HSTs) is nonlinear and uncertain; hence, with the decrease in the running interval of HSTs, an accurate and safe train operation control algorithm is required. In this study, an adaptive output feedback trajectory tracking control method for HSTs is proposed on the basis of neural network observers. The proposed method aims to solve problems, such as the immeasurable speed, model parameter disturbance, and unknown external disturbance of HSTs. In this method, a neural network adaptive observer is designed to estimate the velocity of an HST. Another neural network model is used to approximate the model uncertainties. Moreover, a robust controller is constructed by considering the train position and velocity tracking errors. In the proposed observer/controller, the bound function of estimator errors is introduced to increase the accuracy and safety of the tracking system. Furthermore, the adaptive update value of the neural networks, output weights, and bound function are performed online. All adaptive algorithms and the observer/controller are synthesized in nonlinear control systems. The error signals of the closed-loop trajectory tracking system are uniformly and eventually bounded through a formal proof on the basis of the Lyapunov methods. Simulation examples illustrate that the proposed controller is robust and has excellent tracking accuracy for system model parameter and external disturbance.


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