Adaptive Control for Fractional-Order Micro-Electro-Mechanical Resonator With Nonsymmetric Dead-Zone Input

2015 ◽  
Vol 10 (6) ◽  
Author(s):  
Xiaomin Tian ◽  
Shumin Fei
Keyword(s):  
Adaptive Control ◽  
Fractional Order ◽  
Dead Zone ◽  
Lyapunov Stability Theory ◽  
Distributed Model ◽  
Mechanical Resonator ◽  
Unknown Parameters ◽  
The Dead ◽  
Resonator System ◽  
The Stability

This paper deals with the adaptive control of fractional-order micro-electro-mechanical resonator system (FOMEMRS) with nonsymmetric dead-zone nonlinear input. The slope parameters of the dead-zone nonlinearity are unmeasured and the parameters of the controlled systems are assumed to be unknown in advance. To deal with these unknown parameters, some fractional versions of parametric update laws are proposed. On the basis of the frequency distributed model of fractional integrator and Lyapunov stability theory, a robust control law is designed to prove the stability of the closed-loop system. The proposed adaptive approach requires only the information of bounds of the dead-zone slopes and treats the time-varying input coefficient as a system uncertainty. Finally, simulation examples are given to verify the robustness and effectiveness of the proposed control scheme.

scholarly journals Anti-synchronization of fractional order chaotic and hyperchaotic systems with fully unknown parameters using modified adaptive control

Open Physics ◽  
2016 ◽  
Vol 14 (1) ◽  
pp. 304-313 ◽  
Author(s):  
M. Mossa Al-Sawalha ◽  
Ayman Al-Sawalha
Keyword(s):  
Adaptive Control ◽  
Dynamical Systems ◽  
Theoretical Analysis ◽  
Fractional Order ◽  
Sufficient Conditions ◽  
Lyapunov Stability Theory ◽  
Unknown Parameters ◽  
Adaptive Laws ◽  
Analytic Expression ◽  
Hyperchaotic Systems

AbstractThe objective of this article is to implement and extend applications of adaptive control to anti-synchronize different fractional order chaotic and hyperchaotic dynamical systems. The sufficient conditions for achieving anti–synchronization are derived by using the Lyapunov stability theory and an analytic expression of the controller with its adaptive laws of parameters is shown. Theoretical analysis and numerical simulations are shown to verify the results.

scholarly journals Adaptive Stabilization of a Fractional-Order System with Unknown Disturbance and Nonlinear Input via a Backstepping Control Technique

Symmetry ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 55
Author(s):  
Xiaomin Tian ◽  
Zhong Yang
Keyword(s):  
Fractional Order ◽  
Dead Zone ◽  
External Disturbance ◽  
Lyapunov Theory ◽  
Fractional Order System ◽  
Control Technique ◽  
Order System ◽  
Distributed Model ◽  
Adaptive Stabilization ◽  
Unknown Parameters

In this paper, a new backstepping-based adaptive stabilization of a fractional-order system with unknown parameters is investigated. We assume that the controlled system is perturbed by external disturbance, the bound of external disturbance to be unknown in advance. Moreover, the effects of sector and dead-zone nonlinear inputs both are taken into account. A fractional-order auxiliary system is established to generate the necessary signals for compensation the nonlinear inputs. Meantime, in order to deal with these unknown parameters, some fractional-order adaption laws are given. The frequency-distributed model is used so that the indirect Lyapunov theory is available in designing controllers. Finally, simulation results are presented to verify the effectiveness and robustness of the proposed control strategy.

scholarly journals Adaptive Neural Network Control of a Class of Fractional Order Uncertain Nonlinear MIMO Systems with Input Constraints

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-15 ◽  
Author(s):  
Changhui Wang ◽  
Mei Liang ◽  
Yongsheng Chai
Keyword(s):  
Neural Network ◽  
Fractional Order ◽  
Mimo Systems ◽  
Dead Zone ◽  
Multiple Input Multiple Output ◽  
Lyapunov Stability Theory ◽  
Network Control ◽  
Distributed Model ◽  
Adaptive Neural Network Control ◽  
Input Multiple Output

An adaptive backstepping control scheme for a class of incommensurate fractional order uncertain nonlinear multiple-input multiple-output (MIMO) systems subjected to constraints is discussed in this paper, which ensures the convergence of tracking errors even with dead-zone and saturation nonlinearities in the controller input. Combined with backstepping and adaptive technique, the unknown nonlinear uncertainties are approximated by the radial basis function neural network (RBF NN) in each step of the backstepping procedure. Frequency distributed model of a fractional integrator and Lyapunov stability theory are used for ensuring asymptotic stability of the overall closed-loop system under input dead-zone and saturation. Moreover, the parameter update laws with incommensurate fractional order are used in the controller to compensate unknown nonlinearities. Two simulation results are presented at the end to ensure the efficacy of the proposed scheme.

scholarly journals Adaptive Synchronization between Fractional-Order Chaotic Real and Complex Systems with Unknown Parameters

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Xiaomin Tian
Keyword(s):  
Complex Systems ◽  
Fractional Order ◽  
Lyapunov Stability Theory ◽  
Order Type ◽  
Robust Adaptive Control ◽  
Projective Synchronization ◽  
Adaptive Synchronization ◽  
Distributed Model ◽  
Unknown Parameters ◽  
Constant Matrix

The complex modified projective synchronization (CMPS) between fractional-order chaotic real and complex systems is investigated for the first time. The parameters of both master and slave systems are assumed to be unknown in advance; moreover, the slave system is perturbed by unknown but bounded external disturbances. The master and slave systems that achieved CMPS can be synchronized up to a complex constant matrix. On the basis of frequency distributed model of fractional integrator and Lyapunov stability theory, a robust adaptive control law is designed to realize the CMPS for two different types of fractional-order chaotic systems. Meanwhile, to deal with these unknown parameters, some fractional-order type parametric update laws are provided. An example is given to demonstrate the effectiveness and feasibility of the proposed synchronization scheme.

scholarly journals Universal Projective Synchronization of Two Different Hyperchaotic Systems with Unknown Parameters

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Baojie Zhang ◽  
Hongxing Li
Keyword(s):  
Adaptive Control ◽  
Chaotic Systems ◽  
Control Method ◽  
Scaling Function ◽  
Lyapunov Stability Theory ◽  
Projective Synchronization ◽  
Reference Systems ◽  
Unknown Parameters ◽  
Hyperchaotic Systems ◽  
Function Matrix

Universal projective synchronization (UPS) of two chaotic systems is defined. Based on the Lyapunov stability theory, an adaptive control method is derived such that UPS of two different hyperchaotic systems with unknown parameters is realized, which is up to a scaling function matrix and three kinds of reference systems, respectively. Numerical simulations are used to verify the effectiveness of the scheme.

scholarly journals Adaptive Projective Synchronization between Two Different Fractional-Order Chaotic Systems with Fully Unknown Parameters

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Liping Chen ◽  
Shanbi Wei ◽  
Yi Chai ◽  
Ranchao Wu
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Projective Synchronization ◽  
Control Law ◽  
Unknown Parameters ◽  
Chen System ◽  
Fractional Order Differential Equations ◽  
Response Systems ◽  
The Stability ◽  
Adaptive Control Law

Projective synchronization between two different fractional-order chaotic systems with fully unknown parameters for drive and response systems is investigated. On the basis of the stability theory of fractional-order differential equations, a suitable and effective adaptive control law and a parameter update rule for unknown parameters are designed, such that projective synchronization between the fractional-order chaotic Chen system and the fractional-order chaotic Lü system with unknown parameters is achieved. Theoretical analysis and numerical simulations are presented to demonstrate the validity and feasibility of the proposed method.

Robust Synchronization of Fractional-Order Arneodo Chaotic Systems Using a Fractional Sliding Mode Control Strategy

2018 ◽  
pp. 1-22
Author(s):  
Samir Ladaci ◽  
Karima Rabah ◽  
Mohamed Lashab
Keyword(s):  
Sliding Mode Control ◽  
Fractional Order ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Chaotic Behavior ◽  
Control Design ◽  
Lyapunov Stability Theory ◽  
Mode Control ◽  
Control Configuration ◽  
The Stability

This chapter investigates a new control design methodology for the synchronization of fractional-order Arneodo chaotic systems using a fractional-order sliding mode control configuration. This class of nonlinear fractional-order systems shows a chaotic behavior for a set of model parameters. The stability analysis of the proposed fractional-order sliding mode control law is performed by means of the Lyapunov stability theory. Simulation examples on fractional-order Arneodo chaotic systems synchronization are provided in presence of disturbances and noises. These results illustrate the effectiveness and robustness of this control design approach.

Function Projective Dual Synchronization with Uncertain Parameters of Hyperchaotic Systems

2017 ◽  
Vol 6 (4) ◽  
pp. 1-16 ◽  
Author(s):  
A. Almatroud Othman ◽  
M.S.M. Noorani ◽  
M. Mossa Al-sawalha
Keyword(s):  
Adaptive Control ◽  
Lyapunov Stability Theory ◽  
Control Law ◽  
Uncertain Parameters ◽  
Unknown Parameters ◽  
Chen System ◽  
Response Systems ◽  
Hyperchaotic Lu System ◽  
Hyperchaotic Systems ◽  
Adaptive Control Law

Function projective dual synchronization between two pairs of hyperchaotic systems with fully unknown parameters for drive and response systems is investigated. On the basis of the Lyapunov stability theory, a suitable and effective adaptive control law and parameters update rule for unknown parameters are designed, such that function projective dual synchronization between the hyperchaotic Chen system and the hyperchaotic Lü system with unknown parameters is achieved. Theoretical analysis and numerical simulations are presented to demonstrate the validity and feasibility of the proposed method.

scholarly journals Weighted Multiple-Model Neural Network Adaptive Control for Robotic Manipulators with Jumping Parameters

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-12 ◽  
Author(s):  
Jiazhi Li ◽  
Weicun Zhang ◽  
Quanmin Zhu
Keyword(s):  
Neural Network ◽  
Adaptive Control ◽  
External Disturbance ◽  
Lyapunov Stability Theory ◽  
Robotic Manipulators ◽  
Adaptive Observer ◽  
Multiple Model ◽  
Neural Network Controller ◽  
The Neural Network ◽  
The Stability

This study addresses the tracking control issue for n-link robotic manipulators with largely jumping parameters. Based on radial basis function neural networks (RBFNNs), we propose weighted multiple-model neural network adaptive control (WMNNAC) approach. To cover the variation ranges of the parameters, different models of robotic are constructed. Then, the corresponding local neural network controller is constructed, in which the neural network has been used to approximate the uncertainty part of the control law, and an adaptive observer is implemented to estimate the true external disturbance. The WMNNAC strategy with improved weighting algorithm is adopted to ensure the tracking performance of the robotic manipulator system when parameters jump largely. Through the Lyapunov stability theory and the method of virtual equivalent system (VES), the stability of the closed-loop system is proved. Finally, the simulation results of a two-link manipulator verify the feasibility and efficiency of the proposed WMNNAC strategy.

scholarly journals Amplitude Modulation and Synchronization of Fractional-Order Memristor-Based Chua's Circuit

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
A. G. Radwan ◽  
K. Moaddy ◽  
I. Hashim
Keyword(s):  
Fractional Order ◽  
Amplitude Modulation ◽  
Lyapunov Stability Theory ◽  
Stability And Convergence ◽  
Chua’S Circuit ◽  
Nonlinear Controller ◽  
Chua's Circuit ◽  
Control Functions ◽  
Nonlinear Control Theory ◽  
The Stability

This paper presents a general synchronization technique and an amplitude modulation of chaotic generators. Conventional synchronization and antisynchronization are considered a very narrow subset from the proposed technique where the scale between the output response and the input response can be controlled via control functions and this scale may be either constant (positive, negative) or time dependent. The concept of the proposed technique is based on the nonlinear control theory and Lyapunov stability theory. The nonlinear controller is designed to ensure the stability and convergence of the proposed synchronization scheme. This technique is applied on the synchronization of two identical fractional-order Chua's circuit systems with memristor. Different examples are studied numerically with different system parameters, different orders, and with five alternative cases where the scaling functions are chosen to be positive/negative and constant/dynamic which covers all possible cases from conventional synchronization to the amplitude modulation cases to validate the proposed concept.

Sign in / Sign up

Export Citation Format

Share Document