Direct adaptive dynamic compensation for minimum phase systems with unknown relative degree

Jesse B. Hoagg, Dennis S. Bernstein

Research output: Contribution to journalArticlepeer-review

20 Citations (SciVal)


We consider parameter-monotonic direct adaptive control for single-input-single-output minimum-phase linear time-invariant systems with knowledge of the sign of the high-frequency gain (first nonzero Markov parameter) and an upper bound on the magnitude of the high-frequency gain. The first part of the paper is devoted to fixed-gain analysis of single-parameter high-gain-stabilizing controllers. Two novel fixed-gain dynamic compensators are presented for stabilizing minimum-phase systems. One compensator stabilizes systems with arbitrary-but-known relative degree, while the other utilizes a Fibonacci series construction to stabilize systems with unknown-but-bounded relative degree. Next, we provide a general treatment of parameter-monotonic adaptive control, including a result that guarantees state convergence to zero. This result is then combined with the high-gain-stabilizing controllers to yield parameter-monotonic direct adaptive dynamic compensation for minimum-phase systems with either arbitrary-but-known or unknown-but-bounded relative degree.

Original languageEnglish
Pages (from-to)610-621
Number of pages12
JournalIEEE Transactions on Automatic Control
Issue number4
StatePublished - Apr 2007


  • Adaptive control
  • Fibonacci
  • Parameter monotonic
  • Relative degree

ASJC Scopus subject areas

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


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