Discrete-time adaptive command following and disturbance rejection with unknown exogenous dynamics

Jesse B. Hoagg, Mario A. Santillo, Dennis S. Bernstein

Research output: Contribution to journalArticlepeer-review

114 Scopus citations

Abstract

We present an adaptive controller that requires limited model information for stabilization, command following, and disturbance rejection for mult-input multi-output minimum-phase discrete-time systems. Specifically, the controller requires knowledge of the open-loop system's relative degree as well as a bound on the first nonzero Markov parameter. Notably, the controller does not require knowledge of the command or the disturbance spectrum as long as the command and disturbance signals are generated by a Lyapunov-stable linear system. Thus, the command and disturbance signals are combinations of discrete-time sinusoids and steps. In addition, the Markov-parameter-based adaptive controller uses feedback action only, and thus does not require a direct measurement of the command or disturbance signals. Using a logarithmic Lyapunov function, we prove global asymptotic convergence for command following and disturbance rejection as well as Lyapunov stability of the adaptive system when the open-loop system is asymptotically stable.

Original languageEnglish
Pages (from-to)912-928
Number of pages17
JournalIEEE Transactions on Automatic Control
Volume53
Issue number4
DOIs
StatePublished - May 2008

Keywords

  • Adaptive control
  • Discrete time
  • Lyapunov stability

ASJC Scopus subject areas

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

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