scholarly journals Robust Adaptive Control of Two Chaotic Systems with Unknown Parameters

Author(s):  
Rui-qi WANG ◽  
Ke-jian CHEN ◽  
Jun-yuan GU
Author(s):  
JIANPING CAI ◽  
LUJUAN SHEN ◽  
FUZHEN WU

We consider a class of uncertain non-linear systems preceded by unknown backlash-like hysteresis, which is modelled by a differential equation. We propose a new state feedback robust adaptive control scheme using a backstepping technique and properties of the differential equation. In this control scheme, we construct a new continuous function to design an estimator to estimate the unknown constant parameters and the unknown bound of a ‘disturbance-like’ term. The transient performance of the output tracking error can be guaranteed by the introduction of pre-estimates of the unknown parameters in our controller together with update laws. We do not require bounds on the ‘disturbance-like’ term or unknown system parameters in this scheme. The global stability of the closed-loop system can be proved.


2016 ◽  
Vol 13 (03) ◽  
pp. 1650010 ◽  
Author(s):  
Zhengcai Cao ◽  
Longjie Yin ◽  
Yili Fu ◽  
Jian S. Dai

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.


2020 ◽  
Vol 10 (24) ◽  
pp. 8875 ◽  
Author(s):  
Assef Zare ◽  
Seyede Zeynab Mirrezapour ◽  
Majid Hallaji ◽  
Afshin Shoeibi ◽  
Mahboobeh Jafari ◽  
...  

In this paper, a robust adaptive control strategy is proposed to synchronize a class of uncertain chaotic systems with unknown time delays. Using Lyapunov theory and Lipschitz conditions in chaotic systems, the necessary adaptation rules for estimating uncertain parameters and unknown time delays are determined. Based on the proposed adaptation rules, an adaptive controller is recommended for the robust synchronization of the aforementioned uncertain systems that prove the robust stability of the proposed control mechanism utilizing the Lyapunov theorem. Finally, to evaluate the proposed robust and adaptive control mechanism, the synchronization of two Jerk chaotic systems with finite non-linear uncertainty and external disturbances as well as unknown fixed and variable time delays are simulated. The simulation results confirm the ability of the proposed control mechanism in robust synchronization of the uncertain chaotic systems as well as to estimate uncertain and unknown parameters.


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