Invariant Manifolds Based Modular Adaptive Control for a Class of Nonlinear Systems with Application to Flight Control

2013 ◽  
Vol 373-375 ◽  
pp. 1488-1492
Author(s):  
Chao Zhang ◽  
Sheng Xiu Zhang ◽  
Yi Nan Liu
Keyword(s):  
Adaptive Control ◽  
Flight Control ◽  
Invariant Manifolds ◽  
Controller Design ◽  
Estimation Error ◽  
Dynamical Behavior ◽  
Unknown Parameters ◽  
Adaptive Controllers ◽  
New Class ◽  
New Type

In this paper a novel modular framework for adaptive control for a class of nonlinear system is developed and applied to flight controller design. The framework is based on the invariant manifolds approach with a new type of reduced-order estimator which allows for stable dynamics to be assigned to the estimation error. We show that this method can be applied to systems with unknown parameters, leading to a new class of modular adaptive controllers which is easier to tune compared to controllers obtained using the classical adaptive approaches and does not suffer from unpredictable dynamical behavior of the parameter update laws.

Allee’s Effect Bifurcation in Generalized Logistic Maps

2019 ◽  
Vol 29 (03) ◽  
pp. 1950039
Author(s):  
J. Leonel Rocha ◽  
Abdel-Kaddous Taha
Keyword(s):  
Allee Effect ◽  
Dynamical Behavior ◽  
Complete Classification ◽  
Unimodal Maps ◽  
New Class ◽  
New Type ◽  
Local And Global Bifurcations ◽  
One Dimensional Maps ◽  
Necessary And Sufficient

This paper concerns the study of the Allee effect on the dynamical behavior of a new class of generalized logistic maps. The fundamentals of the dynamics of this 4-parameter family of one-dimensional maps are presented. A complete classification of the nature and stability of its fixed points is provided. The main results relate to the Allee effect bifurcation: a new type of bifurcation introduced for this class of unimodal maps. A necessary and sufficient condition so that the Allee fixed point is a snap-back repeller is established. In addition, in the parameters space is defined an Allee’s effect region, which determines the existence of an essential extinction for the generalized logistic maps. Local and global bifurcations of generalized logistic maps are investigated.

Robust Adaptive Control for Vision-Based Stabilization of a Wheeled Humanoid Robot

2016 ◽  
Vol 13 (03) ◽  
pp. 1650010 ◽  
Author(s):  
Zhengcai Cao ◽  
Longjie Yin ◽  
Yili Fu ◽  
Jian S. Dai
Keyword(s):  
Adaptive Control ◽  
Humanoid Robot ◽  
Controller Design ◽  
Robust Adaptive Control ◽  
Lyapunov Theory ◽  
Control Technique ◽  
Robot Kinematics ◽  
Unknown Parameters ◽  
Actuator Dynamics ◽  
Robust Adaptive

A significant amount of work has been reported in the area of vision-based stabilization of wheeled robots during the last decade. However, almost all the contributions have not considered the actuator dynamics in the controller design. Considering the unknown parameters of the robot kinematics and dynamics incorporating the actuator dynamics, this paper presents a vision-based robust adaptive controller for the stabilization of a wheeled humanoid robot by using the adaptive backstepping approach. For the controller design, the idea of backstepping is used and the adaptive control technique is applied to treat all parametric uncertainties. Moreover, to attenuate the effect of the external disturbances on control performance, smooth robust compensators are employed. The stability of the proposed control system is analyzed by using Lyapunov theory. Finally, simulation results are given to verify the effectiveness of the proposed controller.

scholarly journals Outer Synchronization of a Modified Quorum-Sensing Network via Adaptive Control

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Jianbao Zhang ◽  
Wenyin Zhang ◽  
Denghua Zhang ◽  
Chengdong Yang ◽  
Kongwei Zhu ◽  
...  
Keyword(s):  
Adaptive Control ◽  
Quorum Sensing ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Lyapunov Stability Theory ◽  
Negative Effects ◽  
Unknown Parameters ◽  
Adaptive Controllers ◽  
Outer Synchronization ◽  
Noise Disturbances

Motivated by the quorum-sensing mechanism of bacteria, this paper modifies the network model by adding unknown parameters and noise disturbances and investigates the problem of outer synchronization via adaptive control. In case there exist three unknown parameters, updating laws are presented to identify the unknown parameters with help of Lyapunov stability theory, and the negative effects of noise disturbances are also compensated by designing adaptive controllers. In addition, we simplify the obtained conditions and carry out two succinct and utilitarian corollaries. Finally, numerical simulations are provided to show the validity of the obtained results.

scholarly journals An Improved Adaptive Tracking Controller of Permanent Magnet Synchronous Motor

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Tat-Bao-Thien Nguyen ◽  
Teh-Lu Liao ◽  
Hang-Hong Kuo ◽  
Jun-Juh Yan
Keyword(s):  
Permanent Magnet ◽  
Neural Control ◽  
Controller Design ◽  
Estimation Error ◽  
Permanent Magnet Synchronous Motor ◽  
Parameter Tuning ◽  
Synchronous Motor ◽  
Unknown Parameters ◽  
Control Scheme ◽  
Fuzzy Neural

This paper proposes a new adaptive fuzzy neural control to suppress chaos and also to achieve the speed tracking control in a permanent magnet synchronous motor (PMSM) drive system with unknown parameters and uncertainties. The control scheme consists of fuzzy neural and compensatory controllers. The fuzzy neural controller with online parameter tuning is used to estimate the unknown nonlinear models and construct linearization feedback control law, while the compensatory controller is employed to attenuate the estimation error effects of the fuzzy neural network and ensure the robustness of the controlled system. Moreover, due to improvement in controller design, the singularity problem is surely avoided. Finally, numerical simulations are carried out to demonstrate that the proposed control scheme can successfully remove chaotic oscillations and allow the speed to follow the desired trajectory in a chaotic PMSM despite the existence of unknown models and uncertainties.

scholarly journals BIFURCATIONS AND LIMIT DYNAMICS IN ADAPTIVE CONTROL SYSTEMS

2005 ◽  
Vol 15 (05) ◽  
pp. 1641-1664 ◽  
Author(s):  
G. R. ROKNI LAMOOKI ◽  
S. TOWNLEY ◽  
H. M. OSINGA
Keyword(s):  
Adaptive Control ◽  
Control Systems ◽  
Closed Loop ◽  
Initial Conditions ◽  
Adaptive Stabilization ◽  
Unknown Parameters ◽  
Adaptive Controllers ◽  
Limit System ◽  
Adaptive Control Systems ◽  
Second Order Systems

Adaptive controllers are used in systems where one or more parameters are unknown. Such controllers are designed to stabilize the system using an estimate for the unknown parameters that is adapted automatically as part of the stabilization. One drawback in adaptive control design is the possibility that the closed-loop limit system is not stable. The worst situation is the existence of a destabilized limit system attracting a large open subset of initial conditions. These situations lie behind bad behavior of the closed-loop adaptive control system. The main issue in this paper is to identify and characterize the occurrence of such bad behavior in the adaptive stabilization of first- and second-order systems with one unknown parameter. We develop normal forms for all possible cases and find the conditions that lead to bad behavior. In this context, we discuss a number of bifurcation-like phenomena.

scholarly journals Key Technology Optimization and Development of New Energy Enterprises of Photovoltaic Power Generation

2021 ◽  
Author(s):  
Jiangping Nan
Keyword(s):  
Adaptive Control ◽  
Control Algorithm ◽  
Direct Method ◽  
Estimation Error ◽  
Random Noise ◽  
Harmonic Distortion ◽  
Current Control ◽  
Harmonic Amplitude ◽  
Unknown Parameters ◽  
Adaptive Control Algorithm

In order to improve the algorithm of time-varying parameters and unknown parameters adaptability, avoid assuming the approximate part deviation caused by the algorithm, this paper proposes a adaptive control algorithm, the algorithm based on lyapunov direct method to predict the output voltage in the process of estimating each parameter in a reasonable manner to parameter estimation error with the actual output current and current automatic adjustment. The adaptive control of current tracking is realized and the error caused by assuming voltage or current and neglecting line resistance is avoided in the predictive current control algorithm. The simulation results show that the tracking current can track the target current with high precision from t = 0 in the presence of random noise, and the power factor is close to 1, showing a good steady-state performance. Frequency domain waveform, the calculated harmonic distortion rate is 2.2418%, waveform quality is good and each harmonic amplitude is small. Conclusion: adaptive control algorithm can quickly and accurately realize current tracking and greatly suppress the noise.

scholarly journals Adaptive Control of a Vehicular Platoon with Unknown Parameters and Input Variations

2020 ◽  
Vol 53 (2) ◽  
pp. 13876-13881
Author(s):  
Mohammad Pourmahmood Aghababa ◽  
Mehrdad Saif ◽  
Bahram Shafai
Keyword(s):  
Adaptive Control ◽  
Unknown Parameters

scholarly journals New class of Lindley distributions: properties and applications

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Duha Hamed ◽  
Ahmad Alzaghal
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Simulation Study ◽  
Likelihood Estimation ◽  
Statistical Properties ◽  
Data Sets ◽  
Lifetime Data ◽  
Unknown Parameters ◽  
Lindley Distribution ◽  
New Class

AbstractA new generalized class of Lindley distribution is introduced in this paper. This new class is called the T-Lindley{Y} class of distributions, and it is generated by using the quantile functions of uniform, exponential, Weibull, log-logistic, logistic and Cauchy distributions. The statistical properties including the modes, moments and Shannon’s entropy are discussed. Three new generalized Lindley distributions are investigated in more details. For estimating the unknown parameters, the maximum likelihood estimation has been used and a simulation study was carried out. Lastly, the usefulness of this new proposed class in fitting lifetime data is illustrated using four different data sets. In the application section, the strength of members of the T-Lindley{Y} class in modeling both unimodal as well as bimodal data sets is presented. A member of the T-Lindley{Y} class of distributions outperformed other known distributions in modeling unimodal and bimodal lifetime data sets.

Study on the working state of the five hundred-meter aperture spherical telescope using step-wise assignment method

2014 ◽  
Vol 229 (2) ◽  
pp. 316-324 ◽  
Author(s):  
Yu Liu ◽  
Feng Gao
Keyword(s):  
Nonlinear Equations ◽  
Analytical Solutions ◽  
Driving Mechanism ◽  
Initial Value ◽  
Unknown Parameters ◽  
Support Structure ◽  
Assignment Method ◽  
New Type ◽  
Set Up ◽  
The Mathematical Model

The working state of the five hundred-meter aperture spherical telescope (FAST) is solved using the step-wise assignment method. In this paper, the mathematical model of the cable-net support structure of the FAST is set up by the catenary equation. There are a large number of nonlinear equations and unknown parameters of the model. The nonlinear equations are solved by using the step-wise assignment method. The method is using the analytical solutions of the cable-net equations of one working state as the initial value for the next working state, from which the analytical solutions of the nonlinear equations of the cable-net for each working state of the FAST and the tension and length of each driving cable can be obtained. The suggested algorithm is quite practically well suited to study the working state of the cable-net structures of the FAST. Also, the working state analysis result of the cable-net support structure of a reduced model of the cable-net structure reflector for the FAST is given to verify the reliability of the method. In order to show the validity of the method, comparisons with another algorithm to set the initial value are presented. This method has an important guiding significance to the further study on the control of the new type of flexible cable driving mechanism, especially the FAST.

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