scholarly journals Exponential stabilization of a linear Korteweg-de Vries equation with input saturation

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Ahmat Mahamat Taboye ◽  
Mohamed Laabissi
Keyword(s):  
Exponential Stability ◽  
Closed Loop ◽  
Vries Equation ◽  
Input Saturation ◽  
Loop System ◽  
Exponential Stabilization ◽  
Closed Loop System ◽  
De Vries ◽  
Exponentially Stable ◽  
Well Posed

<p style='text-indent:20px;'>This article deals with the issue of the exponential stability of a linear Korteweg-de Vries equation with input saturation. It is proved that the system is well-posed and the origin is exponentially stable for the closed loop system, by using the classical argument used in this kind of problems.</p>

scholarly journals Adaptive Stabilization of the Korteweg-de Vries-Burgers Equation with Unknown Dispersion

2012 ◽  
Vol 2012 ◽  
pp. 1-12
Author(s):  
Xiaoyan Deng ◽  
Lixin Tian ◽  
Wenxia Chen
Keyword(s):  
Closed Loop ◽  
Burgers Equation ◽  
Loop System ◽  
Adaptive Stabilization ◽  
Closed Loop System ◽  
Dynamic Component ◽  
Barbalat’S Lemma ◽  
Lyapunov Function Method ◽  
De Vries ◽  
Well Posed

This paper studies the adaptive control problem of the Korteweg-de Vries-Burgers equation. Using the Lyapunov function method, we prove that the closed-loop system including the parameter estimator as a dynamic component is globallyL2stable. Furthermore, we show that the state of the system is regulated to zero by developing an alternative to Barbalat's lemma which cannot be used in the present situation. The closed-loop system is shown to be well posed.

scholarly journals Exponential Stability of the Monotubular Heat Exchanger Equation with Time Delay in Boundary Observation

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Xue-Lian Jin ◽  
Yang Zhang ◽  
Fu Zheng ◽  
Bao-zhu Guo
Keyword(s):  
Heat Exchanger ◽  
Time Delay ◽  
Exponential Stability ◽  
Closed Loop ◽  
Abstract Cauchy Problem ◽  
Loop System ◽  
Physical Parameters ◽  
Closed Loop System ◽  
Close Loop System ◽  
Resolvent Estimates

The exponential stability of the monotubular heat exchanger equation with boundary observation possessing a time delay and inner control was investigated. Firstly, the close-loop system was translated into an abstract Cauchy problem in the suitable state space. A uniformly bounded C0-semigroup generated by the close-loop system, which implies that the unique solution of the system exists, was shown. Secondly, the spectrum configuration of the closed-loop system was analyzed and the eventual differentiability and the eventual compactness of the semigroup were shown by the resolvent estimates on some resolvent sets. This implies that the spectrum-determined growth assumption holds. Finally, a sufficient condition, which is related to the physical parameters in the system and is independent of the time delay, of the exponential stability of the closed-loop system was given.

scholarly journals Sector stability criteria for a nonlinear axial motion string system

2021 ◽  
Author(s):  
Rui Wu ◽  
Yi Cheng ◽  
Donal O'Regan
Keyword(s):  
Exponential Stability ◽  
Closed Loop ◽  
Semigroup Theory ◽  
Nonlinear Partial Differential Equation ◽  
Loop System ◽  
Closed Loop System ◽  
Axially Moving ◽  
The Right ◽  
Nonlinear Semigroup Theory ◽  
Control Criterion

The paper investigates the exponential stability criterion for an axially moving string system driven by a nonlinear partial differential equation with nonlinear boundary feedback.The control criterion based on a sector condition contains a large class of nonlinearities, which is a negative feedback of the velocity at the right boundary of the moving string. By invoking nonlinear semigroup theory, the well-posedness result of the closed-loop system is verified under the sector criteria. Furthermore, a novel energy like function is constructed to establish the exponential stability of the closed-loop system by using a integral-type multiplier method and the generalized Gronwall-type integral inequality.

scholarly journals Actuator Saturation and Control Design for Buildings Structural Systems with Improved Uncertainty Description

2013 ◽  
Vol 20 (2) ◽  
pp. 297-308 ◽  
Author(s):  
Y.C. Ding ◽  
F.L. Weng ◽  
Z.A. Yu
Keyword(s):  
Closed Loop ◽  
Actuator Saturation ◽  
Input Saturation ◽  
Lyapunov Theory ◽  
Loop System ◽  
Structural Systems ◽  
Control Input ◽  
Closed Loop System ◽  
Parameter Uncertainties ◽  
Earthquake Excitation

The problem of robustly active vibration control for a class of earthquake-excited structural systems with time-delay and saturation in the control input channel and parameter uncertainties appearing in all the mass, damping and stiffness matrices is concerned in this paper. The objective of the designing controllers is to guarantee the robust stability of the closed-loop system and attenuate the disturbance from earthquake excitation. Firstly, by using the linear combination of some matrices to deal with the system's uncertainties, a new system uncertainties description, namely rank-1 uncertainty description, is presented. Then, by introducing a linear varying parameter, the input saturation model is described as a linear parameter varying model. Furthermore, based on parameter-dependent Lyapunov theory and linear matrix inequality (LMI) technique, the LMIs-based conditions for the closed-loop system to be stable are deduced. By solving those conditions, the controller, considering the actuator saturation, input delay and parameters uncertainties, is obtained. Finally, a three-storey linear building structure under earthquake excitation is considered and simulation results are given to show the effectiveness of the proposed controllers.

scholarly journals Boundary Stabilization of Heat Equation with Multi-Point Heat Source

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 834
Author(s):  
Qing-Qing Hu ◽  
Feng-Fei Jin ◽  
Bao-Qiang Yan
Keyword(s):  
Heat Source ◽  
Heat Equation ◽  
Exponential Stability ◽  
Output Feedback ◽  
Closed Loop ◽  
Feedback Controller ◽  
Loop System ◽  
Boundary Stabilization ◽  
Closed Loop System ◽  
Point Heat Source

In this paper, we consider boundary stabilization problem of heat equation with multi-point heat source. Firstly, a state feedback controller is designed mainly by backstepping approach. Under the designed state controller, the exponential stability of closed-loop system is guaranteed. Then, an observer-based output feedback controller is proposed. We prove the exponential stability of resulting closed-loop system using operator semigroup theory. Finally, the designed state and output feedback controllers are effective via some numerical simulations.

scholarly journals Exponential stability of axially moving Kirchhoff-beam systems with nonlinear boundary damping and disturbance

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yi Cheng ◽  
Zhihui Dong ◽  
Donal O' Regan
Keyword(s):  
Exponential Stability ◽  
Closed Loop ◽  
Initial Conditions ◽  
Galerkin Approximation ◽  
Nonlinear Damping ◽  
Loop System ◽  
Direct Lyapunov Method ◽  
Closed Loop System ◽  
Uniqueness Of Solutions ◽  
Axially Moving

<p style='text-indent:20px;'>This paper examines the stabilization problem of the axially moving Kirchhoff beam. Under the nonlinear damping criterion established by the slope-restricted condition, the existence and uniqueness of solutions of the closed-loop system equipped with nonlinear time-delay disturbance at the boundary is investigated via the Faedo-Galerkin approximation method. Furthermore, the solution is continuously dependent on initial conditions. Then the exponential stability of the closed-loop system is established by the direct Lyapunov method, where a novel energy function is constructed.</p>

scholarly journals Adaptive Leader-Follower Formation Control of Under-actuated Surface Vessels with Model Uncertainties and Input Constraints

2019 ◽  
Vol 9 (18) ◽  
pp. 3901 ◽  
Author(s):  
Riahifard ◽  
Hosseini Rostami ◽  
Wang ◽  
Kim
Keyword(s):  
Formation Control ◽  
Closed Loop ◽  
Input Saturation ◽  
Small Neighborhood ◽  
Loop System ◽  
Input Constraints ◽  
Closed Loop System ◽  
Model Uncertainties ◽  
Autonomous Surface Vehicles ◽  
Autonomous Surface Vehicle

This paper deals with the leader-follower formation control of underactuated autonomous surface vehicles in the presence of model uncertainties and input constraints. In a leader-follower formation, an autonomous surface vehicle (ASV) called leader tracks a pre-described trajectory and other ASVs called followers that are controlled to follow the leader with a desired distance and desired relative bearing. To this end, some adaptive robust techniques are adopted to guarantee the robustness of the closed-loop system against model uncertainties, external disturbances, and input saturation constraints. Based on the Lyapunov synthesis, it is proven that with the developed formation controllers, the closed-loop system is stable and all the formation errors converge to a small neighborhood of zero. Simulation results demonstrate the effectiveness of the proposed method.

Abstract #254 Analysis of the Pivotal Trial Data of the MinimedTM 670G Hybrid Closed-Loop System in Adults, Adolescents and Children with Type 1 Diabetes Using Novel Composite Metrics

2019 ◽  
Vol 25 ◽  
pp. 96
Author(s):  
Robert Vigersky ◽  
Andreas Thomas ◽  
John Shin ◽  
Boyi Jiang ◽  
Chantal McMahon
Keyword(s):  
Type 1 Diabetes ◽  
Closed Loop ◽  
Trial Data ◽  
Loop System ◽  
Pivotal Trial ◽  
Closed Loop System

Closed-Loop System Improves Glucose Control

2010 ◽  
Vol 40 (4) ◽  
pp. 42-43
Author(s):  
MIRIAM E. TUCKER
Keyword(s):  
Glucose Control ◽  
Closed Loop ◽  
Loop System ◽  
Closed Loop System

Safety and Performance of the Omnipod®Hybrid Closed-Loop System in Adolescents with Type 1 Diabetes over Five Days Under Free-Living Conditions

Diabetes ◽  
2018 ◽  
Vol 67 (Supplement 1) ◽  
pp. 1376-P
Author(s):  
GREGORY P. FORLENZA ◽  
BRUCE BUCKINGHAM ◽  
JENNIFER SHERR ◽  
THOMAS A. PEYSER ◽  
JOON BOK LEE ◽  
...  
Keyword(s):  
Type 1 Diabetes ◽  
Closed Loop ◽  
Living Conditions ◽  
Loop System ◽  
Closed Loop System ◽  
Free Living ◽  
And Performance ◽  
Free Living Conditions
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