NDLI: Adaptive Control? But is so Simple! : A Tribute to the Efficiency, Simplicity and Beauty of Adaptive Control

Content Provider	Springer Nature Link
Author	Barkana, Itzhak
Copyright Year	2015
Abstract	In a recent paper, a few pioneers of adaptive control review the classical model reference adaptive control (MRAC) concept, where the designer is basically supposed to conceive a model of the same order as the (possibly very large) plant, and then build an adaptive controller such that the plant is stable and ultimately follows the behavior of the model. Basically, adaptive control methods based on model following assume full-state feedback or full-order observers or identifiers. These assumptions, along with supplementary prior knowledge, allowed the first rigorous proofs of stability with adaptive controllers, which at the time was a very important first result. However, in order to obtain this important mathematical result, the developers of classical MRAC took the useful scalar Optimal Control feedback signal and made it into an adaptive gain-vector of basically of the same order as the plant, which again had to multiply the plant state-vector in order to finally end with another scalar adaptive control feedback signal. It is quite known today, however, what happens when this requirement is not satisfied, and when “unmodeled dynamics” distorts the controller based on these ideal assumptions. Even though much effort has been invested to maintain stability in spite of so-called “unmodeled dynamics,” in some applications, such as large flexible structures and other real-world applications, even if one can assume that the order of the plant is known, one just cannot implement a controller of the same order as the plant (or even a “nominal” or a “dominant” part of the plant), before even mentioning the complexity of such an adaptive controller. Without entering the argument around their special reserve in relation to claimed efficiency of the particular L1-Adaptive Control methodology, this paper first shows that, after the first successful proof of stability and even under the same basic full-state availability assumption, the adaptive control itself can be reduced to just one adaptive gain (which multiplies one error signal) in single-input-single-output (SISO) systems and, as a straightforward extension, an m*m gain matrix in an m-input-m-output (MIMO) plant. Not only is stability not affected, but actually the simplified scheme also gets rid of most seemingly “inherent” problems of the adaptive control represented by classical MRAC. Moreover, proofs of stability have all been based on the so-called Barbalat’s lemma which seems to require very strict uniform continuity of signals. The apparent implications are that any discontinuity, such as square-wave input commands or just some occasionally discontinuous disturbance, may put stability of adaptive control in danger, without even mentioning such things as impulse response. Instead, based on old yet amazingly unknown extensions of LaSalle’s Invariance Principle to nonautonomous nonlinear systems, recent developments in stability analysis of nonlinear systems have mitigated or even eliminated most apparently necessary prior conditions, thus adding confidence in the robustness of adaptive scheme in real world situations.
Starting Page	3
Ending Page	34
Page Count	32
File Format	PDF
ISSN	09210296
Journal	Journal of Intelligent & Robotic Systems
Volume Number	83
Issue Number	1
e-ISSN	15730409
Language	English
Publisher	Springer Netherlands
Publisher Date	2015-10-26
Publisher Place	Dordrecht
Access Restriction	Subscribed
Subject Keyword	Control systems Adaptive control Stability Nonlinear systems Autonomous and nonautonomous systems Control, Robotics, Mechatronics Electrical Engineering Artificial Intelligence (incl. Robotics) Mechanical Engineering
Content Type	Text
Resource Type	Article
Subject	Industrial and Manufacturing Engineering Artificial Intelligence Control and Systems Engineering Mechanical Engineering Electrical and Electronic Engineering Software

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

Special Issue on Autonomous Robot Systems

Autonomous Robot Systems : Guest Editorial

Autonomous Autorotation of Unmanned Rotorcraft using Nonlinear Model Predictive Control

An Adaptable Oscillator-Based Controller for Autonomous Robots

Simulation Validation of Three Nonlinear Model-Based Controllers in the Adaptive Cruise Control System

Adaptive Nonlinear Stabilization Control for a Quadrotor UAV: Theory, Simulation and Experimentation

Sliding Mode Neuro Adaptive Control in Trajectory Tracking for Mobile Robots

Wind Estimation for Accurate Airplane Path Following Applications

Advanced Robotics

Adaptive Control? But is so Simple! : A Tribute to the Efficiency, Simplicity and Beauty of Adaptive Control

Similar Documents

Special Issue on Autonomous Robot Systems

Autonomous Robot Systems : Guest Editorial

Autonomous Autorotation of Unmanned Rotorcraft using Nonlinear Model Predictive Control

An Adaptable Oscillator-Based Controller for Autonomous Robots

Simulation Validation of Three Nonlinear Model-Based Controllers in the Adaptive Cruise Control System

Adaptive Nonlinear Stabilization Control for a Quadrotor UAV: Theory, Simulation and Experimentation

Sliding Mode Neuro Adaptive Control in Trajectory Tracking for Mobile Robots

Wind Estimation for Accurate Airplane Path Following Applications

Advanced Robotics

Adaptive Control? But is so Simple! : A Tribute to the Efficiency, Simplicity and Beauty of Adaptive Control