Guaranteed Transient Performance with L1 Adaptive Controller for Systems with Unknown Time-varying Parameters and Bounded Disturbances: Part I

2007 ◽  
Author(s):  
Chengyu Cao ◽  
Naira Hovakimyan
Keyword(s):  
Adaptive Controller ◽  
Time Varying ◽  
Transient Performance ◽  
Varying Parameters ◽  
Time Varying Parameters ◽  
Bounded Disturbances ◽  
L1 Adaptive Controller

Adaptive Control of Mechanical Systems With Time-Varying Parameters and Disturbances

2004 ◽  
Vol 126 (3) ◽  
pp. 520-530 ◽  
Author(s):  
Prabhakar R. Pagilla ◽  
Yongliang Zhu
Keyword(s):  
Adaptive Control ◽  
Finite Length ◽  
Mechanical Systems ◽  
Adaptive Controller ◽  
Projection Algorithm ◽  
Time Interval ◽  
Time Varying ◽  
Varying Parameters ◽  
Time Varying Parameter ◽  
Time Varying Parameters

A new adaptive control algorithm for mechanical systems with time-varying parameters and/or time-varying disturbances is proposed and investigated. The proposed method does not assume any structure to the time-varying parameter or disturbance. The method is based on the expansion of the time-varying parameter/disturbance using Taylor’s formula. This facilitates expanding a time-varying function as a finite length polynomial and a bounded residue. The coefficients of the finite-length polynomial are estimated in a small time interval so that they can be assumed to be constant within that interval. A gradient projection algorithm is used to estimate the parameters within each time interval. Stability of the proposed adaptive controller is shown and discussed. A novel experiment is designed using a two-link planar mechanical manipulator to investigate the proposed algorithm experimentally. Results of the proposed adaptive controller are compared with an ideal nonadaptive controller that assumes complete knowledge of the parameters and disturbances. A representative sample of the experimental results is shown and discussed.

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.

Synchronization of Chaotic Systems with Uncertain Time-Varying Parameters

2015 ◽  
Vol 9 (6) ◽  
pp. 568
Author(s):  
Ahmad Al-Jarrah ◽  
Mohammad Ababneh ◽  
Suleiman Bani Hani ◽  
Khalid Al-Widyan
Keyword(s):  
Chaotic Systems ◽  
Time Varying ◽  
Varying Parameters ◽  
Time Varying Parameters ◽  
Uncertain Time
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