barbalat’s lemma
Recently Published Documents


TOTAL DOCUMENTS

42
(FIVE YEARS 17)

H-INDEX

9
(FIVE YEARS 2)

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Tahir Khan ◽  
Zi-Shan Qian ◽  
Roman Ullah ◽  
Basem Al Alwan ◽  
Gul Zaman ◽  
...  

We investigate and analyze the dynamics of hepatitis B with various infection phases and multiple routes of transmission. We formulate the model and then fractionalize it using the concept of fractional calculus. For the purpose of fractionalizing, we use the Caputo–Fabrizio operator. Once we develop the model under consideration, existence and uniqueness analysis will be discussed. We use fixed point theory for the existence and uniqueness analysis. We also prove that the model under consideration possesses a bounded and positive solution. We then find the basic reproductive number to perform the steady-state analysis and to show that the fractional-order epidemiological model is locally and globally asymptotically stable under certain conditions. For the local and global analysis, we use linearization, mean value theorem, and fractional Barbalat’s lemma, respectively. Finally, we perform some numerical findings to support the analytical work with the help of graphical representations.


Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2284
Author(s):  
Xuemiao Chen ◽  
Ziwen Wu ◽  
Jing Li ◽  
Qianjin Zhao

In this paper, for a class of uncertain stochastic nonlinear systems with input time-varying delays, an adaptive neural dynamic surface control (DSC) method is proposed. To approximate the unknown continuous functions online, the neural network approximation technique was applied, and based on the DSC scheme, the desired controller was constructed. A compensation system is presented to compensate for the effect of the input delay. The Lyapunov–Krasovskii functionals (LKFs) were employed to compensate for the effect of the state delay. Compared with the existing works, based on using the DSC scheme with the nonlinear filter and stochastic Barbalat’s lemma, the asymptotic regulation performance of this closed-loop system can be guaranteed under the developed controller. To certify the availability for the designed control method, some simulation results are presented.


2021 ◽  
Vol 2 ◽  
Author(s):  
Sulong Li ◽  
Qin Wang ◽  
Enci Wang ◽  
Yangyang Chen

In this paper, the bearing-only formation control problem of a class of second-order system with unknown disturbance is investigated, where the control law merely depends on the relative bearings between neighboring agents. In order to offset the effect of unknown disturbance on the system, adaptive estimation is introduced. In the design of the control law, the back-stepping design method and the negative gradient method are used. The Barbalat’s lemma is used to prove the global stability of the system. The simulation results prove the effectiveness of the proposed formation control algorithm.


Author(s):  
Ce Liu ◽  
Junyong Zhai

This article concentrates on the output feedback controller design for a class of stochastic nonlinear systems with unknown homogeneous growth rates. First, a full-order observer is proposed coupling with a dynamic gain so as to obtain system state estimates. Then, an adaptive output feedback controller is put forward by the homogeneity theory and adding a power integrator technique. Combined with the stochastic Barbalat’s lemma, the signals of the closed-loop system are demonstrated to be bounded and all the system states are proved to converge to the origin in probability. Besides, the results are also expanded to the controller design of upper-triangular stochastic nonlinear system. Two simulation results indicate usefulness of the designed control algorithm.


2021 ◽  
Author(s):  
Tingting Cheng ◽  
Ben Niu ◽  
Guangju Zhang ◽  
Zhenhua Wang ◽  
Peiyong Duan

Abstract This paper formulates an event-triggered adaptive asymptotic tracking control scheme for flexible robotic manipulators via command filtered backstepping method. Firstly, in the proposed design algorithm, the unknown nonlinear functions are firstly approximated by using intelligent estimation technique. Then, the “explosion of complexity” problem existing in the traditional backstepping procedure is solved by cleverly applying the command filtered backstepping method. In addition, an event-triggered mechanism is adopted so that the control input is updated irregularly following the occurrence of an event. The advantages of the proposed adaptive design scheme are as follows: (i) the Barbalat’s Lemma is used to asymptotically drive the tracking error to zero; (ii) all the variables in the closed-loop system are bounded; (iii) the utilized event-triggered mechanism reduces the transmission frequency of computer and saves computer resources. Finally, the simulation results of the robotic system are given to illustrate the effectiveness of our design scheme.


2020 ◽  
Vol 10 (24) ◽  
pp. 8806
Author(s):  
Chih-Chen Yih ◽  
Shih-Jeh Wu

This paper aims to deal with the problem of robot tracking control in the presence of parametric uncertainties in kinematics and dynamics. We propose a simple and effective adaptive control scheme that includes adaptation laws for unknown constant kinematic and dynamic parameters. In addition, instead of convolution-type filtered differentiation, we designed a new observer to estimate velocity in the task space, and the proposed adaptive control requires no acceleration measurement in the joint space. Using the Lyapunov stability and Barbalat’s lemma, we show that by appropriately choosing design parameters, the tracking errors and estimation errors in task space can asymptotically converge to zero. Through numerical simulation on a two-link robot with a fixed camera, we illustrate the design procedures and demonstrate the feasibility of the proposed adaptive control scheme for the trajectory tracking of robot manipulators.


Author(s):  
Mihua Ma ◽  
Jianping Cai

An intermittent controller for robotic manipulator in the presence of dynamic uncertainties was developed in this paper. The adaptation law is designed to deal with the dynamic uncertainties. In task space, for given a desired position, the robot end-effector is able to reach the desired position under the designed intermittent controller. Different from most of the existing works on control of robotic manipulator, the designed controller only needs to receive the information of the desired position in some interval time, but not continuously. In addition, the intermittent control of robotic manipulator is discussed in task space instead of joint space. Based on an extended Barbalat’s Lemma, some simple control gains are obtained. As a direct application, we implement the proposed controller on a two-link robotic manipulator. Numerical simulations demonstrate the effectiveness of the proposed control strategy.


Author(s):  
Salahudden ◽  
Vijay S Dwivedi ◽  
Prasiddha N Dwivedi ◽  
Dipak K Giri ◽  
Ajoy K Ghosh

In the present paper, a control command to recover steady-straight-level flight from flat-oscillatory-stable-left-spin is developed using a sliding-mode based attitude and altitude control. Direct spin recovery, using a spin solution by bifurcation results, to low angle-of-attack is achieved in finite-time without any separation in dynamics. The exponential convergence of errors is discussed by invoking Barbalat’s Lemma theorem. Thereafter settling time is obtained thereby making the system a finite-time stable to reach the sliding surface. The novelty of this work lies in the proposed control strategy, wherein expressions for all four primary control inputs are obtained in a closed-loop form without any approximation and altitude margin required for flat-spin recovery is investigated based on a heuristic approach for a fixed controller gains. Additionally, results of this research indicate the proposed controller first stops the spin by controlling the attitude of the aircraft thereby rotation stops about the body axis and then reaches the commanded altitude to attain the horizontal flight.


2020 ◽  
pp. 002029402094496
Author(s):  
Huimin Ouyang ◽  
Xiang Xu ◽  
Guangming Zhang

In the control research on the rotary crane systems with double-pendulum effect, a motion trajectory with both simple structure and excellent robust performance is proposed to achieve the positioning of the boom and the suppression of the load sway. The presented trajectory consists of an anti-swing component and a boom positioning component, where the first part is used to achieve the sway angle elimination without affecting boom positioning; the second one is used to move the boom to the desired location precisely. The Lyapunov technique, LaSalle’s invariance theorem, and Barbalat’s lemma are used to prove the excellent performance of the method. Eventually, the effectiveness of the proposed method was verified through a large amount of simulation data analysis.


Sign in / Sign up

Export Citation Format

Share Document