Dynamic scaling and observer design with application to adaptive control

Automatica ◽  
2009 ◽  
Vol 45 (12) ◽  
pp. 2883-2889 ◽  
Author(s):  
Dimitrios Karagiannis ◽  
Mario Sassano ◽  
Alessandro Astolfi
Keyword(s):  
Adaptive Control ◽  
Observer Design ◽  
Dynamic Scaling

scholarly journals Implicit Regularization and Momentum Algorithms in Nonlinearly Parameterized Adaptive Control and Prediction

2021 ◽  
Vol 33 (3) ◽  
pp. 590-673
Author(s):  
Nicholas M. Boffi ◽  
Jean-Jacques E. Slotine
Keyword(s):  
Adaptive Control ◽  
Nonlinear Control ◽  
Adaptive Dynamics ◽  
Observer Design ◽  
Local Geometry ◽  
Natural Gradient ◽  
Lagrange Equations ◽  
First Order ◽  
Adaptive Nonlinear Control ◽  
Mirror Descent

Stable concurrent learning and control of dynamical systems is the subject of adaptive control. Despite being an established field with many practical applications and a rich theory, much of the development in adaptive control for nonlinear systems revolves around a few key algorithms. By exploiting strong connections between classical adaptive nonlinear control techniques and recent progress in optimization and machine learning, we show that there exists considerable untapped potential in algorithm development for both adaptive nonlinear control and adaptive dynamics prediction. We begin by introducing first-order adaptation laws inspired by natural gradient descent and mirror descent. We prove that when there are multiple dynamics consistent with the data, these non-Euclidean adaptation laws implicitly regularize the learned model. Local geometry imposed during learning thus may be used to select parameter vectors—out of the many that will achieve perfect tracking or prediction—for desired properties such as sparsity. We apply this result to regularized dynamics predictor and observer design, and as concrete examples, we consider Hamiltonian systems, Lagrangian systems, and recurrent neural networks. We subsequently develop a variational formalism based on the Bregman Lagrangian. We show that its Euler Lagrange equations lead to natural gradient and mirror descent-like adaptation laws with momentum, and we recover their first-order analogues in the infinite friction limit. We illustrate our analyses with simulations demonstrating our theoretical results.

Finite-time convergent observer design and adaptive control of a nonlinear boiler system

2012 ◽  
Author(s):  
Johnathan Votion ◽  
Chuanlin Zhang ◽  
Chunjiang Qian ◽  
Shihua Li
Keyword(s):  
Adaptive Control ◽  
Finite Time ◽  
Observer Design

Non-certainty equivalent adaptive control for lower triangular systems based on dynamic scaling and filter

2013 ◽  
Vol 27 (12) ◽  
pp. 1097-1106 ◽  
Author(s):  
Shengtao Li ◽  
Yuanwei Jing ◽  
Xiaomei Liu
Keyword(s):  
Adaptive Control ◽  
Certainty Equivalent ◽  
Dynamic Scaling ◽  
Triangular Systems ◽  
Lower Triangular

A Constructive Procedure based on Dynamic Scaling for Adaptive Control of Nonlinearly Parameterized Nonlinear Systems

2011 ◽  
Vol 44 (1) ◽  
pp. 120-125
Author(s):  
Xiangbin Liu ◽  
Romeo Ortega ◽  
Hongye Su ◽  
Jian Chu
Keyword(s):  
Adaptive Control ◽  
Nonlinear Systems ◽  
Dynamic Scaling ◽  
Nonlinearly Parameterized

Comments on 'An adaptive control scheme for robot manipulators'

1989 ◽  
Vol 49 (5) ◽  
pp. 1805-1809
Author(s):  
Yong-Duan Song ◽  
Wei-Bing Gao
Keyword(s):  
Adaptive Control ◽  
Robot Manipulators ◽  
Control Scheme ◽  
Adaptive Control Scheme
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