Tracking with prescribed transient behaviour

Achim Ilchmann, E. P. Ryan, C. J. Sangwin

Research output: Contribution to journalArticlepeer-review


Universal tracking control is investigated in the context of a class S of M-input, M-output dynamical systems modelled by functional differential equations. The class encompasses a wide variety of nonlinear and infinite-dimensional systems and contains - as a prototype subclass - all finite-dimensional linear single-input single-output minimum-phase systems with positive high-frequency gain. The control objective is to ensure that, for an arbitrary RM-valued reference signal r of class W1,∞ (absolutely continuous and bounded with essentially bounded derivative) and every system of class S, the tracking error e between plant output and reference signal evolves within a prespecified performance envelope or funnel in the sense that θ(t)∥e(t)∥ < 1 for all t ≥ 0, where θ a prescribed real-valued function of class W1,∞ with the property that θ(s) > 0 for all s > 0 and lim infs→∞ θ(s) > 0. A simple (neither adaptive nor dynamic) error feedback control of the form u(t) = -α(θ(t)∥e(t)∥)e(t) is introduced which achieves the objective whilst maintaining boundedness of the control and of the scalar gain α(θ(·)∥e(·)∥).

Original languageEnglish
Pages (from-to)471-493
Number of pages23
JournalESAIM: Control, Optimisation and Calculus of Variations
Publication statusPublished - 2002


  • Feedback control
  • Functional differential equations
  • Nonlinear systems
  • Tracking
  • Transient behaviour

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