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

<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>

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Sector stability criteria for a nonlinear axial motion string system

10.22541/au.161944403.39426300/v1 ◽

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.

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Dynamic Image-Based Visual Servo Control Using Centroid and Optic Flow Features

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.2807085 ◽

2007 ◽

Vol 130 (1) ◽

Cited By ~ 50

Author(s):

R. Mahony ◽

P. Corke ◽

T. Hamel

Keyword(s):

Optic Flow ◽

Closed Loop ◽

Initial Conditions ◽

Adaptive Estimation ◽

Loop System ◽

Servo Control ◽

Visual Servo ◽

Closed Loop System ◽

Visual Servo Control ◽

Vision Measurement

This paper considers the question of designing a fully image-based visual servo control for a class of dynamic systems. The work is motivated by the ongoing development of image-based visual servo control of small aerial robotic vehicles. The kinematics and dynamics of a rigid-body dynamical system (such as a vehicle airframe) maneuvering over a flat target plane with observable features are expressed in terms of an un-normalized spherical centroid and an optic flow measurement. The image-plane dynamics with respect to force input are dependent on the height of the camera above the target plane. This dependence is compensated by introducing virtual height dynamics and adaptive estimation in the proposed control. A fully nonlinear adaptive control design is provided that ensures asymptotic stability of the closed-loop system for all feasible initial conditions. The choice of control gains is based on an analysis of the asymptotic dynamics of the system. Results from a realistic simulation are presented that demonstrate the performance of the closed-loop system. To the author’s knowledge, this paper documents the first time that an image-based visual servo control has been proposed for a dynamic system using vision measurement for both position and velocity.

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Application of Anytime Control to an Inherently Unstable Physical System

Volume 4A: Dynamics, Vibration, and Control ◽

10.1115/imece2015-51369 ◽

2015 ◽

Author(s):

Wayne Maxwell ◽

Al Ferri ◽

Bonnie Ferri

Keyword(s):

Closed Loop ◽

Initial Conditions ◽

Transient Behavior ◽

Open Loop ◽

Loop System ◽

Closed Loop System ◽

Pendulum System ◽

Inverted Pendulum System ◽

Lqr Controller ◽

Two Stages

This paper extends the use of closed-loop anytime control to systems that are inherently unstable in the open-loop. Previous work has shown that anytime control is very effective in compensating for occasional missed deadlines in the computer processor. When misses occur, the control law is truncated or partially executed. However, the previous work assumed that the open-loop system was stable. In this paper, the anytime strategy is applied to an inverted pendulum system. An LQR controller with estimated state feedback is designed and decomposed into two stages. Both stages are implemented most of the time, but in a small percentage of time, only the first stage is applied, with the resulting closed-loop system being unstable for short periods of time. The statistical performance of the closed-loop system is studied using Monte-Carlo simulations. It is seen that, on average, the closed-loop performance is very close to that of the full-order controller as long as the miss rate is relatively small. However, the variance of the response shows much higher dependence on the miss rate, suggesting that the response becomes more unpredictable. At a critical value of miss rate, the closed-loop system is unstable. The critical miss rate found through simulation is seen to correlate well with the results of a deterministic stability analysis. The statistics on the settling time are also studied, and shown to grow longer as the miss rate increases. The transient behavior of the system is studied for a range of initial conditions.

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

Mathematical Problems in Engineering ◽

10.1155/2017/8952647 ◽

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.

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Boundary Stabilization of Heat Equation with Multi-Point Heat Source

Mathematics ◽

10.3390/math9080834 ◽

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.

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

Evolution Equations and Control Theory ◽

10.3934/eect.2021052 ◽

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>

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