The bang-bang funnel controller for uncertain nonlinear systems with arbitrary relative degree

Daniel M Liberzon, Stephan Trenn

Research output: Contribution to journalArticlepeer-review


The paper considers output tracking control of uncertain nonlinear systems with arbitrary known relative degree and known sign of the high frequency gain. The tracking objective is formulated in terms of a time-varying bound - a funnel - around a given reference signal. The proposed controller is bang-bang with two control values. The controller switching logic handles arbitrarily high relative degree in an inductive manner with the help of auxiliary derivative funnels. We formulate a set of feasibility assumptions under which the controller maintains the tracking error within the funnel. Furthermore, we prove that under mild additional assumptions the considered system class satisfies these feasibility assumptions if the selected control values are sufficiently large in magnitude. Finally, we study the effect of time delays in the feedback loop and we are able to show that also in this case the proposed bang-bang funnel controller works under slightly adjusted feasibility assumptions.

Original languageEnglish (US)
Article number6578131
Pages (from-to)3126-3141
Number of pages16
JournalIEEE Transactions on Automatic Control
Issue number12
StatePublished - Dec 1 2013


  • Bang-bang control
  • Nonlinear systems
  • Uncertain systems

ASJC Scopus subject areas

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

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