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Transient bounds for adaptive control systems

Adaptive control systems are essentially nonlinear and mechanisms to analyze their stability and transient response typically derive from more general nonlinear theories such as small gain arguments or passivity. In this note, we consider how these theories may be applied to adaptive control to quan...

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Published in:	IEEE transactions on automatic control 1994-01, Vol.39 (1), p.171-175
Main Authors:	Zhuquan Zang, Bitmead, R.R.
Format:	Article
Language:	English
Subjects:	Adaptative systems Adaptive control Adaptive systems Applied sciences Computer science control theory systems Control systems Control theory. Systems Controllability Error correction Exact sciences and technology Nonlinear control systems Robustness Signal analysis Stability Transient response
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container_title	IEEE transactions on automatic control
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creator	Zhuquan Zang Bitmead, R.R.
description	Adaptive control systems are essentially nonlinear and mechanisms to analyze their stability and transient response typically derive from more general nonlinear theories such as small gain arguments or passivity. In this note, we consider how these theories may be applied to adaptive control to quantify transient response. This involves the explicit description of the constants appearing in the passivity theorem and/or the small gain theorem which characterize both system gains and initial condition effects. The result is a fundamental connection between transient response bounds and uniform plant controllability, which connects initial state conditions with the input-output analysis. Applying these general theorems to adaptive control, we are able to interpret the uniform controllability condition as a persistency of excitation requirement and thereby to provide local bounds on transient response. The implication of these sufficient results is that without both bounds upon initial conditions and guarantees of excitation, potentially extreme transient excursions of system variables are possible even though global convergence and asymptotic performance are guaranteed.< >
doi_str_mv	10.1109/9.273360
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In this note, we consider how these theories may be applied to adaptive control to quantify transient response. This involves the explicit description of the constants appearing in the passivity theorem and/or the small gain theorem which characterize both system gains and initial condition effects. The result is a fundamental connection between transient response bounds and uniform plant controllability, which connects initial state conditions with the input-output analysis. Applying these general theorems to adaptive control, we are able to interpret the uniform controllability condition as a persistency of excitation requirement and thereby to provide local bounds on transient response. 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The implication of these sufficient results is that without both bounds upon initial conditions and guarantees of excitation, potentially extreme transient excursions of system variables are possible even though global convergence and asymptotic performance are guaranteed.< ></description><subject>Adaptative systems</subject><subject>Adaptive control</subject><subject>Adaptive systems</subject><subject>Applied sciences</subject><subject>Computer science; control theory; systems</subject><subject>Control systems</subject><subject>Control theory. Systems</subject><subject>Controllability</subject><subject>Error correction</subject><subject>Exact sciences and technology</subject><subject>Nonlinear control systems</subject><subject>Robustness</subject><subject>Signal analysis</subject><subject>Stability</subject><subject>Transient response</subject><issn>0018-9286</issn><issn>1558-2523</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1994</creationdate><recordtype>article</recordtype><recordid>eNqFkE1LAzEQhoMoWKvg2dMeRLxsTSYfmxyl-AUFL_UcstkEVrabmtkK_feubOm1p2GYh4d3XkJuGV0wRs2TWUDFuaJnZMak1CVI4OdkRinTpQGtLskV4ve4KiHYjJTr7HpsQz8Uddr1DRYx5cI1bju0v6HwqR9y6grc4xA2eE0uousw3BzmnHy9vqyX7-Xq8-1j-bwqPVdqKAUTQiqjYi0MUzUXrJHOeRgzeBliA4YKznntIGoXteSu5lBJ0UhglFPG5-Rh8m5z-tkFHOymRR-6zvUh7dCOAs2ggtOgVhWtlDoNVqDHDHoEHyfQ54SYQ7Tb3G5c3ltG7X_D1tip4RG9PzgdetfFsUnf4pHnBpSC_2fuJqwNIRyvB8cf4Ih_9A</recordid><startdate>199401</startdate><enddate>199401</enddate><creator>Zhuquan Zang</creator><creator>Bitmead, R.R.</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</general><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>8FD</scope><scope>H8D</scope><scope>L7M</scope><scope>7SC</scope><scope>7SP</scope><scope>7TB</scope><scope>FR3</scope><scope>JQ2</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>199401</creationdate><title>Transient bounds for adaptive control systems</title><author>Zhuquan Zang ; Bitmead, R.R.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c366t-41445696fb4916b341d5aac2018c5efd2904333ba2f8af853ab32754d52103013</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1994</creationdate><topic>Adaptative systems</topic><topic>Adaptive control</topic><topic>Adaptive systems</topic><topic>Applied sciences</topic><topic>Computer science; control theory; systems</topic><topic>Control systems</topic><topic>Control theory. Systems</topic><topic>Controllability</topic><topic>Error correction</topic><topic>Exact sciences and technology</topic><topic>Nonlinear control systems</topic><topic>Robustness</topic><topic>Signal analysis</topic><topic>Stability</topic><topic>Transient response</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Zhuquan Zang</creatorcontrib><creatorcontrib>Bitmead, R.R.</creatorcontrib><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts</collection><collection>Electronics & Communications Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>IEEE transactions on automatic control</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Zhuquan Zang</au><au>Bitmead, R.R.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Transient bounds for adaptive control systems</atitle><jtitle>IEEE transactions on automatic control</jtitle><stitle>TAC</stitle><date>1994-01</date><risdate>1994</risdate><volume>39</volume><issue>1</issue><spage>171</spage><epage>175</epage><pages>171-175</pages><issn>0018-9286</issn><eissn>1558-2523</eissn><coden>IETAA9</coden><notes>ObjectType-Article-2</notes><notes>SourceType-Scholarly Journals-1</notes><notes>ObjectType-Feature-1</notes><notes>content type line 23</notes><abstract>Adaptive control systems are essentially nonlinear and mechanisms to analyze their stability and transient response typically derive from more general nonlinear theories such as small gain arguments or passivity. 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source	IEEE Electronic Library (IEL) Journals
subjects	Adaptative systems Adaptive control Adaptive systems Applied sciences Computer science control theory systems Control systems Control theory. Systems Controllability Error correction Exact sciences and technology Nonlinear control systems Robustness Signal analysis Stability Transient response
title	Transient bounds for adaptive control systems
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