Adaptive projection-based observers and L1 adaptive controllers for infinite-dimensional systems with full-state measurement

Vivek Natarajan, Joseph Bentsman

Research output: Contribution to journalArticlepeer-review


Adaptive observers using projection-operator-based parameter update laws are considered for a class of linear infinite-dimensional systems with bounded input operator and full state measurement and subject to time-varying matched uncertainties and disturbances. 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 using the proposed observers. Existence and uniqueness of solutions for the resulting closed loop system and uniform boundedness of the observation error are established first. Then, provided certain assumptions on the plant transfer function and the solution of a Lyapunov inequality hold, uniform guaranteed transient performance bounds on the plant state and control signal under the L1 architecture are derived. Two examples satisfying the assumptions-control of a heat equation and a wave equation-are presented. Reference input tracking simulation results for the heat equation under the L1 adaptive control subject to time-varying matched uncertainties and disturbances are presented in support of the theory.

Original languageEnglish (US)
Article number6644252
Pages (from-to)585-598
Number of pages14
JournalIEEE Transactions on Automatic Control
Issue number3
StatePublished - Mar 2014


  • Adaptive observers
  • distributed parameter systems
  • guaranteed transient performance
  • projection operator
  • time-varying uncertainty

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering

Fingerprint Dive into the research topics of 'Adaptive projection-based observers and L<sub>1</sub> adaptive controllers for infinite-dimensional systems with full-state measurement'. Together they form a unique fingerprint.

Cite this