L1 Adaptive Controller for a Class of Nonlinear Systems

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Jie Luo ◽  
Chengyu Cao
Keyword(s):  
Nonlinear Systems ◽  
Reference System ◽  
Adaptive Controller ◽  
Time Varying ◽  
Robot Arm ◽  
Performance Bounds ◽  
Estimation Errors ◽  
State Dependent ◽  
Low Pass ◽  
L1 Adaptive Controller

This paper presents an extension of the L1 adaptive controller to a class of nonlinear systems where the control effectiveness is time-varying and unknown, but with a known sign. Moreover, this class of nonlinear systems contains time-varying and unknown state-dependent nonlinearities. The proposed L1 adaptive controller consists of three components, a state predictor used to estimate real states, an adaptive law used to update the adaptive parameters in the state predictor, and a low-pass filtered control law. First, the stable closed-loop reference system is constructed. Then, the estimation errors between estimated states and real states are proved to be arbitrarily small by increasing the adaptation rate. After that, we further prove that the adaptive controller ensures uniformly bounded transient and asymptotical tracking of the reference system. The performance bounds can be systematically improved by increasing the adaptation rate. Simulation results on a single-link nonlinear robot arm verify the theoretical findings.

Adaptive Control for Uncertain Hysteretic Systems

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
Xiaotian Zou ◽  
Jie Luo ◽  
Chengyu Cao
Keyword(s):  
Adaptive Control ◽  
Linear Time ◽  
Adaptive Controller ◽  
Time Varying ◽  
Performance Bounds ◽  
L1 Adaptive Control ◽  
Hysteretic Systems ◽  
Time Varying Parameters ◽  
L1 Adaptive Controller ◽  
Uniformly Bounded

This paper presents an approach to use the L1 adaptive controller for a class of uncertain systems in the presence of unknown Preisach-type hysteresis in input, unknown time-varying parameters, and unknown time-varying disturbances. The hysteresis operator can be transformed into an equivalent linear time-varying (LTV) system with uncertainties, which means that the effect of the hysteresis can be considered as general uncertainties to the system. Without constructing the inverse hysteresis function, the L1 adaptive control is used to handle the uncertainties introduced by the hysteresis, as well as system dynamics. The adaptive controller presented in this paper ensures uniformly bounded transient and tracking performance for uncertain hysteretic systems. The performance bounds can be systematically improved by increasing the adaptation rate. Simulation results with Preisach-type hysteresis are provided to verify the theoretical findings.

scholarly journals Complete Periodic Synchronization of Memristor-Based Neural Networks with Time-Varying Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Huaiqin Wu ◽  
Luying Zhang ◽  
Sanbo Ding ◽  
Xueqing Guo ◽  
Lingling Wang
Keyword(s):  
Neural Networks ◽  
Periodic Solution ◽  
Matrix Theory ◽  
Adaptive Controller ◽  
Network System ◽  
Time Varying ◽  
State Dependent ◽  
Coincidence Theorem ◽  
Error System ◽  
Theoretical Results

This paper investigates the complete periodic synchronization of memristor-based neural networks with time-varying delays. Firstly, under the framework of Filippov solutions, by usingM-matrix theory and the Mawhin-like coincidence theorem in set-valued analysis, the existence of the periodic solution for the network system is proved. Secondly, complete periodic synchronization is considered for memristor-based neural networks. According to the state-dependent switching feature of the memristor, the error system is divided into four cases. Adaptive controller is designed such that the considered model can realize global asymptotical synchronization. Finally, an illustrative example is given to demonstrate the validity of the theoretical results.

Robust Adaptive Control of Mildly Nonlinear Systems With Time Varying Input/Output Delays

2012 ◽  
Author(s):  
James P. Nelson ◽  
Mark J. Balas ◽  
Richard S. Erwin
Keyword(s):  
Adaptive Control ◽  
Nonlinear Systems ◽  
Adaptive Controller ◽  
Robust Adaptive Control ◽  
Control Law ◽  
Time Varying ◽  
Robust Adaptive ◽  
Input Delays ◽  
Persistent Disturbances ◽  
Adaptive Control Law

Many systems must operate in the presence of delays both internal to the system and in its inputs and outputs. In this paper we present a robustness result for mildly nonlinear systems. We use this result to show that, for small unknown time varying input delays, a simple adaptive controller can produce output regulation to a neighborhood with radius dependent upon the size of an upper bound on the delay. This regulation occurs in the presence of persistent disturbances and the convergence is exponential. We conclude with an example to illustrate the behavior of this adaptive control law.

Robust Adaptive Control of Uncertain Nonlinear Systems With Time-Varying Input Delay

2017 ◽  
Author(s):  
W. X. Deng ◽  
J. Y. Yao
Keyword(s):  
Nonlinear Systems ◽  
Controller Design ◽  
Adaptive Controller ◽  
Robust Adaptive Control ◽  
Input Delay ◽  
Time Varying ◽  
Uncertain Nonlinear Systems ◽  
Bounded Disturbances ◽  
Robust Adaptive ◽  
Adaptive Feedforward

In this paper, a robust adaptive controller is proposed for a class of uncertain nonlinear systems subject to time-varying input delay, parametric uncertainties and additive bounded disturbances. The desired trajectory based adaptive feedforward technique and a predictor-like robust delay compensating term are integrated via backstepping in the controller design. The proposed controller theoretically ensures semi-global uniformly ultimately bounded tracking performance based on Lyapunov stability analysis by employing Lyapunov-Krasovskii (LK) functionals. Simulation results are obtained to illustrate the effectiveness of the proposed control strategy.

Adaptive tracking control of stochastic nonlinear systems with unknown time-varying powers

2021 ◽  
pp. 014233122098223
Author(s):  
Huijuan Li ◽  
Wuquan Li ◽  
Jianzhong Gu
Keyword(s):  
Nonlinear Systems ◽  
Design Method ◽  
Tracking Error ◽  
Small Neighborhood ◽  
Adaptive Controller ◽  
Upper And Lower Bounds ◽  
Stochastic Nonlinear Systems ◽  
Time Varying ◽  
Adaptive Tracking Control ◽  
Output Tracking

This paper investigates the adaptive output tracking problem for a class of high-order stochastic nonlinear systems with unknown time-varying powers and nonlinear parameterized uncertainties. By using the parameter separation technique and adding a power integrator design method, an adaptive controller with upper and lower bounds of the unknown time-varying power is successfully designed to guarantee that all the states of the closed-loop system are bounded in probability and the output tracking error can be regulated into a small neighborhood of the origin in probability. Finally, a simulation example is provided to illustrate the effectiveness of the designed controllers.

scholarly journals Dynamic Neural Network Identification and Decoupling Control Approach for MIMO Time-Varying Nonlinear Systems

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Zhixi Shen ◽  
Kai Zhao
Keyword(s):  
Neural Network ◽  
Nonlinear System ◽  
Nonlinear Systems ◽  
Lyapunov Stability Theory ◽  
Adaptive Controller ◽  
Time Varying ◽  
Dynamic Neural Networks ◽  
Control Approach ◽  
The Neural Network ◽  
And Control

Overcoming the coupling among variables is greatly necessary to obtain accurate, rapid and independent control of the real nonlinear systems. In this paper, the main methodology, on which the method is based, is dynamic neural networks (DNN) and adaptive control with the Lyapunov methodology for the time-varying, coupling, uncertain, and nonlinear system. Under the framework, the DNN is developed to accommodate the identification, and the weights of DNN are iteratively and adaptively updated through the identification errors. Based on the neural network identifier, the adaptive controller of complex system is designed in the latter. To guarantee the precision and generality of decoupling tracking performance, Lyapunov stability theory is applied to prove the error between the reference inputs and the outputs of unknown nonlinear system which is uniformly ultimately bounded (UUB). The simulation results verify that the proposed identification and control strategy can achieve favorable control performance.

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