scholarly journals On the Positioning Problem of a Microscopic Particle Trapped in Optical Tweezers

2009 ◽  
Vol 2009 ◽  
pp. 1-16
Author(s):  
Carlos Aguilar-Ibañez ◽  
Luis I. Rosas-Soriano
Keyword(s):  
Optical Tweezers ◽  
Thermal Noise ◽  
Lyapunov Method ◽  
Control Strategies ◽  
Optical Trap ◽  
Lyapunov Stability Theory ◽  
Viscous Force ◽  
Random Position ◽  
Spherical Microparticle ◽  
The Stability

We solve the positioning problem of a spherical microparticle trapped by Optical Tweezers, under the assumption that the drag viscous force is presented. To do it, we develop two control strategies for the manipulation of this kind of optical trap. The first control strategy is developed assuming that the damping coefficient is known, while in the second strategy this parameter value is only partially known, which in practice it is more realistic due to the difficulty to estimate it. Both strategies are based on the traditional Lyapunov method in conjunction with the use of a saturation function. The stability analysis of both strategies was carried out by using the standard Lyapunov stability theory. Finally, numerical simulations validate the effectiveness of both control approaches in reducing the random position fluctuations produced by the inherent thermal noise.

scholarly journals Stability Analysis of Interconnected Fuzzy Systems Using the Fuzzy Lyapunov Method

2010 ◽  
Vol 2010 ◽  
pp. 1-10 ◽  
Author(s):  
Ken Yeh ◽  
Cheng-Wu Chen
Keyword(s):  
Stability Analysis ◽  
Lyapunov Functions ◽  
Fuzzy Systems ◽  
Lyapunov Method ◽  
Lyapunov Stability Theory ◽  
Linear Matrix ◽  
Stability Conditions ◽  
Fuzzy Lyapunov Function ◽  
Quadratic Lyapunov Functions ◽  
The Stability

The fuzzy Lyapunov method is investigated for use with a class of interconnected fuzzy systems. The interconnected fuzzy systems consist ofJinterconnected fuzzy subsystems, and the stability analysis is based on Lyapunov functions. Based on traditional Lyapunov stability theory, we further propose a fuzzy Lyapunov method for the stability analysis of interconnected fuzzy systems. The fuzzy Lyapunov function is defined in fuzzy blending quadratic Lyapunov functions. Some stability conditions are derived through the use of fuzzy Lyapunov functions to ensure that the interconnected fuzzy systems are asymptotically stable. Common solutions can be obtained by solving a set of linear matrix inequalities (LMIs) that are numerically feasible. Finally, simulations are performed in order to verify the effectiveness of the proposed stability conditions in this paper.

A new robust control strategy for axial flux permanent magnet motor applied on legged lunar robots

2021 ◽  
pp. 107754632110564
Author(s):  
Zheng-Han Chen ◽  
Zhao-Dong Xu ◽  
Hong-Fang Lu ◽  
Jian-Zhong Yang ◽  
Deng-Yun Yu ◽  
...  
Keyword(s):  
Permanent Magnet ◽  
Control Strategies ◽  
Lyapunov Stability Theory ◽  
Legged Robots ◽  
Permanent Magnet Motors ◽  
Permanent Magnet Motor ◽  
Axial Flux ◽  
Robust Controller ◽  
External Circumstance ◽  
The Stability

Legged robots have the advantage of strong terrain adaptability in lunar exploration. A new robust controller is designed for axial flux permanent magnet motors applied on the legged lunar robots to diminish the disturbance from uncertainty and external circumstance. The theoretical verification is carried out through Lyapunov stability theory. The numerical simulation and real-time experiment are carried out to access the stability and dynamic property of the systems adopting the proposed controller. The results are compared with the traditional control strategies to demonstrate the advantages of the proposed controller. The new robust controller contributes to the dynamic stability of legged lunar robots and is also appropriate for the similar mechanical systems.

scholarly journals Dynamics of the rumor-spreading model with hesitation mechanism in heterogenous networks and bilingual environment

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Shuai Yang ◽  
Haijun Jiang ◽  
Cheng Hu ◽  
Juan Yu ◽  
Jiarong Li
Keyword(s):  
Lyapunov Method ◽  
Reproduction Number ◽  
Model Parameters ◽  
Rumor Spreading ◽  
Spreading Model ◽  
Reductio Ad Absurdum ◽  
The Stability ◽  
The Impact ◽  
Theoretical Results ◽  
The Basic Reproduction Number

Abstract In this paper, a novel rumor-spreading model is proposed under bilingual environment and heterogenous networks, which considers that exposures may be converted to spreaders or stiflers at a set rate. Firstly, the nonnegativity and boundedness of the solution for rumor-spreading model are proved by reductio ad absurdum. Secondly, both the basic reproduction number and the stability of the rumor-free equilibrium are systematically discussed. Whereafter, the global stability of rumor-prevailing equilibrium is explored by utilizing Lyapunov method and LaSalle’s invariance principle. Finally, the sensitivity analysis and the numerical simulation are respectively presented to analyze the impact of model parameters and illustrate the validity of theoretical results.

Global stability analysis of fractional-order gene regulatory networks with time delay

2019 ◽  
Vol 12 (06) ◽  
pp. 1950067 ◽  
Author(s):  
Zhaohua Wu ◽  
Zhiming Wang ◽  
Tiejun Zhou
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Gene Regulatory Networks ◽  
Existence And Uniqueness ◽  
Regulatory Networks ◽  
Lyapunov Method ◽  
Regulation Mechanism ◽  
Global Stability Analysis ◽  
Gene Regulatory ◽  
The Stability

Fractional-order gene regulatory networks with time delay (DFGRNs) have proven that they are more suitable to model gene regulation mechanism than integer-order. In this paper, a novel DFGRN is proposed. The existence and uniqueness of the equilibrium point for the DFGRN are proved under certain conditions. On this basis, the conditions on the global asymptotic stability are established by using the Lyapunov method and comparison theorem for the DFGRN, and the stability conditions are dependent on the fractional-order [Formula: see text]. Finally, numerical simulations show that the obtained results are reasonable.

scholarly journals Enhanced Signal-to-Noise and Fast Calibration of Optical Tweezers Using Single Trapping Events

Micromachines ◽  
2021 ◽  
Vol 12 (5) ◽  
pp. 570
Author(s):  
Alexander B. Stilgoe ◽  
Declan J. Armstrong ◽  
Halina Rubinsztein-Dunlop
Keyword(s):  
Brownian Motion ◽  
Optical Tweezers ◽  
Optical Trap ◽  
Force Transducer ◽  
Signal To Noise ◽  
Likelihood Estimator ◽  
Micro Fluidics ◽  
Large Numbers ◽  
Force Reconstruction ◽  
Micron Particle

The trap stiffness us the key property in using optical tweezers as a force transducer. Force reconstruction via maximum-likelihood-estimator analysis (FORMA) determines the optical trap stiffness based on estimation of the particle velocity from statistical trajectories. Using a modification of this technique, we determine the trap stiffness for a two micron particle within 2 ms to a precision of ∼10% using camera measurements at 10 kfps with the contribution of pixel noise to the signal being larger the level Brownian motion. This is done by observing a particle fall into an optical trap once at a high stiffness. This type of calibration is attractive, as it avoids the use of a nanopositioning stage, which makes it ideal for systems of large numbers of particles, e.g., micro-fluidics or active matter systems.

ORIENTATING MANIPULATION OF CYLINDRICAL PARTICLES WITH OPTICAL TWEEZERS

2008 ◽  
Vol 17 (04) ◽  
pp. 387-394 ◽  
Author(s):  
XIUDONG SUN ◽  
XUECONG LI ◽  
JIANLONG ZHANG
Keyword(s):  
Escherichia Coli ◽  
Carbon Nanotubes ◽  
Laser Beam ◽  
Optical Tweezers ◽  
Optical Trap ◽  
Polarization Direction ◽  
Beam Shape ◽  
E Coli ◽  
Potential Applications ◽  
Cylindrical Particles

Orientating manipulations of cylindrical particles were performed by optical tweezers. Vertical and horizontal manipulations of Escherichia coli (E. coli) were carried out by changing the trapping depth and the focused laser beam shape. It was found that carbon nanotubes bundles (CNTBs) could be rotated in the linear polarized optical trap until it orientated its long axis along the linear polarization direction of the laser beam. However, E.coli could not be orientated in this way. Corresponding mechanisms were discussed based on the anisomeric electric characters of CNTBs. These orientation technologies of cylindrical objects with optical trap have potential applications in assembling nano-electric devices.

On the stability of a mathematical model for HIV(AIDS) - cancer dynamics

2021 ◽  
Vol 8 (4) ◽  
pp. 783-796
Author(s):  
H. W. Salih ◽  
◽  
A. Nachaoui ◽  
Keyword(s):  
Mathematical Model ◽  
Highly Active Antiretroviral Therapy ◽  
Lyapunov Method ◽  
Equilibrium Points ◽  
Hiv Treatment ◽  
Biochemical Processes ◽  
Highly Active ◽  
Biological Phenomena ◽  
The Stability ◽  
The Impact

In this work, we study an impulsive mathematical model proposed by Chavez et al. [1] to describe the dynamics of cancer growth and HIV infection, when chemotherapy and HIV treatment are combined. To better understand these complex biological phenomena, we study the stability of equilibrium points. To do this, we construct an appropriate Lyapunov function for the first equilibrium point while the indirect Lyapunov method is used for the second one. None of the equilibrium points obtained allow us to study the stability of the chemotherapeutic dynamics, we then propose a bifurcation of the model and make a study of the bifurcated system which contributes to a better understanding of the underlying biochemical processes which govern this highly active antiretroviral therapy. This shows that this mathematical model is sufficiently realistic to formulate the impact of this treatment.

Chaos Control for a Fractional-Order Jerk System via Time Delay Feedback Controller and Mixed Controller

2021 ◽  
Vol 5 (4) ◽  
pp. 257
Author(s):  
Changjin Xu ◽  
Maoxin Liao ◽  
Peiluan Li ◽  
Lingyun Yao ◽  
Qiwen Qin ◽  
...  
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Chaos Control ◽  
Chaotic Behavior ◽  
Control Strategies ◽  
Feedback Controller ◽  
Research Approach ◽  
Controlling Chaos ◽  
The Stability ◽  
Jerk System

In this study, we propose a novel fractional-order Jerk system. Experiments show that, under some suitable parameters, the fractional-order Jerk system displays a chaotic phenomenon. In order to suppress the chaotic behavior of the fractional-order Jerk system, we design two control strategies. Firstly, we design an appropriate time delay feedback controller to suppress the chaos of the fractional-order Jerk system. The delay-independent stability and bifurcation conditions are established. Secondly, we design a suitable mixed controller, which includes a time delay feedback controller and a fractional-order PDσ controller, to eliminate the chaos of the fractional-order Jerk system. The sufficient condition ensuring the stability and the creation of Hopf bifurcation for the fractional-order controlled Jerk system is derived. Finally, computer simulations are executed to verify the feasibility of the designed controllers. The derived results of this study are absolutely new and possess potential application value in controlling chaos in physics. Moreover, the research approach also enriches the chaos control theory of fractional-order dynamical system.

scholarly journals APPLICATION OF LEARNING REINFORCEMENT METHOD IN ROBOTIZED AND AUTOMATED FORESTRY SYSTEMS

2020 ◽  
Vol 10 (1) ◽  
pp. 256-265
Author(s):  
Andrey Tolstyh ◽  
D Stupnikov ◽  
Sergey Malyukov ◽  
Aleksandr Luk'yanov ◽  
Yuriy Lunev
Keyword(s):  
Physical Environment ◽  
Learning Algorithm ◽  
Back Propagation ◽  
Industrial Robots ◽  
Environment Model ◽  
Random Position ◽  
Learning Reinforcement ◽  
The Stability ◽  
Two Stages ◽  
The Cost

Abstract Currently, most large enterprises are actively using industrial robots and other automated solutions. This allows a significant increase in productivity and quality of work performed. This article gave a brief overview of modern industrial robots, their operating principle, basic components and systems. A reinforcement learning algorithm was developed and tested. The task of constructing a learning algorithm with reinforcement was divided into two stages: modeling the environment and description and optimization of the cost function. Since industrial robotic systems operate in the real world, the environment model should reflect basic physical laws. Therefore, the pyBullet library of the physical environment was chosen as the physical environment for testing. After modeling the manipulator in the selected physical medium, it was given the trivial task of touching a given object with the capture of the manipulator. An artificial neural network was used as an agent interacting with the environment. The inputs were the coordinates of the object and the existing angles of rotation of the articulated joints of the robot. Outputs - angle of rotation of joints at this step. This network was trained using the back propagation method, Adam modification. The system was trained for about 12 hours. Success is achieved in 95% of cases when testing the stability of the system (random position of the cylinder). In future, it is planned to test the obtained models on bench samples

Sign in / Sign up

Export Citation Format

Share Document