Tracking with prescribed transient behaviour
ESAIM: Control, Optimisation and Calculus of Variations, Tome 7 (2002), pp. 471-493.

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 M -valued reference signal r of class W 1, (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 ϕ(t)e(t)<1 for all t0, where ϕ a prescribed real-valued function of class W 1, with the property that ϕ(s)>0 for all s>0 and lim inf s ϕ(s)>0. A simple (neither adaptive nor dynamic) error feedback control of the form u(t)=-α(ϕ(t)e(t))e(t) is introduced which achieves the objective whilst maintaining boundedness of the control and of the scalar gain α(ϕ(·)e(·)).

DOI : https://doi.org/10.1051/cocv:2002064
Classification : 93D15,  93C30,  34K20
Mots clés : nonlinear systems, functional differential equations, feedback control, tracking, transient behaviour
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     title = {Tracking with prescribed transient behaviour},
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     url = {http://www.numdam.org/articles/10.1051/cocv:2002064/}
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Ilchmann, Achim; Ryan, E. P.; Sangwin, C. J. Tracking with prescribed transient behaviour. ESAIM: Control, Optimisation and Calculus of Variations, Tome 7 (2002), pp. 471-493. doi : 10.1051/cocv:2002064. http://www.numdam.org/articles/10.1051/cocv:2002064/

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