Adaptive observers with projection operator and L1 adaptive controllers for infinite dimensional systems

Vivek Natarajan, Joseph Bentsman

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Adaptive observers with projection operator based parameter update laws are considered for a class of linear infinite dimensional systems with bounded input operator and full state measurement under constant and time-varying matched uncertainties. The L1 adaptive control architecture, introduced recently for finite dimensional plants to provide guaranteed transient performance via fast adaptation, is then extended to this class. Existence and uniqueness of solution to the closed loop system and asymptotic decay of the observation error are established. Under certain assumptions on the transfer function and on the solution to the Lyapunov inequality, the L 1 architecture is analyzed and uniform bounds on the state and control signal are established. Two examples, a heat equation and a wave equation, satisfying the assumptions are presented.

Original languageEnglish (US)
Title of host publication2012 American Control Conference, ACC 2012
Pages3002-3007
Number of pages6
StatePublished - Nov 26 2012
Event2012 American Control Conference, ACC 2012 - Montreal, QC, Canada
Duration: Jun 27 2012Jun 29 2012

Publication series

NameProceedings of the American Control Conference
ISSN (Print)0743-1619

Other

Other2012 American Control Conference, ACC 2012
CountryCanada
CityMontreal, QC
Period6/27/126/29/12

Keywords

  • L -adaptive control
  • Projection
  • adaptive observers
  • coercivity
  • well-posedness

ASJC Scopus subject areas

  • Electrical and Electronic Engineering

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    Natarajan, V., & Bentsman, J. (2012). Adaptive observers with projection operator and L1 adaptive controllers for infinite dimensional systems. In 2012 American Control Conference, ACC 2012 (pp. 3002-3007). [6315680] (Proceedings of the American Control Conference).