Geometry of adaptive control

Felipe M. Pait, Benedetto Piccoli

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

1 Scopus citations


Two incompatible topologies appear in the study of adaptive systems: The graph topology in control design, and the coefficient topology in system identification. Their incompatibility is manifest in the stabilization problem of adaptive control. We argue that this problem can be approached by changing the geometry of the sets of control systems under consideration: estimating n parameters in an n-dimensional manifold whose points all correspond to stabilizable systems. One way to accomplish this is using the properties of the algebraic Riccati equation. To illustrate the ideas we pose a simple parameter estimation problem as a constrained optimization problem, and show that it admits a unique minimum. Search algorithms in a hypersurface lead to adaptive controllers that combine ideas classified as direct and indirect adaptive control in the literature.

Original languageEnglish (US)
Title of host publication2001 European Control Conference, ECC 2001
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages4
ISBN (Electronic)9783952417362
StatePublished - 2001
Externally publishedYes
Event6th European Control Conference, ECC 2001 - Porto, Portugal
Duration: Sep 4 2001Sep 7 2001

Publication series

Name2001 European Control Conference, ECC 2001


Other6th European Control Conference, ECC 2001

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering


  • Adaptive control
  • Riccati equation
  • system identification
  • topology and geometry of control systems

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