Adaptive control designs for control-based continuation in a class of uncertain discrete-time dynamical systems

Yang Li, Harry Dankowicz

Research output: Contribution to journalArticlepeer-review


This article proposes a methodology for integrating adaptive control with the control-based continuation paradigm for a class of uncertain, linear, discrete-time systems. The proposed adaptive control strategies aim to stabilize the closed-loop dynamics with convergence toward a known reference input, such that the dynamics approach the open-loop fixed point if the reference input is chosen to make the steady-state control input equal 0. This enables the tracking of a parameterized branch of open-loop fixed points using methods of numerical continuation without specific knowledge about the system. We implement two different adaptive control strategies: model-reference adaptive control and pole-placement adaptive control. Both implementations achieve the desired objectives for the closed-loop dynamics and support parameter continuation. These properties, as well as the boundedness of system states and control inputs, are guaranteed provided that certain stability conditions are satisfied. Besides, the tuning effort is significantly reduced in the adaptive control schemes compared with traditional proportional–derivative controllers and linear state-space feedback controllers.

Original languageEnglish (US)
Pages (from-to)2092-2109
Number of pages18
JournalJVC/Journal of Vibration and Control
Issue number21-22
StatePublished - Nov 1 2020


  • Parameter continuation
  • guaranteed transient performance
  • model-reference adaptive control
  • periodic points
  • persistent excitation
  • pole-placement adaptive control

ASJC Scopus subject areas

  • Automotive Engineering
  • General Materials Science
  • Aerospace Engineering
  • Mechanics of Materials
  • Mechanical Engineering


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