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(·)).

Classification : 93D15,  93C30,  34K20
Mots clés : nonlinear systems, functional differential equations, feedback control, tracking, transient behaviour
     author = {Ilchmann, Achim and Ryan, E. P. and Sangwin, C. J.},
     title = {Tracking with prescribed transient behaviour},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {471--493},
     publisher = {EDP-Sciences},
     volume = {7},
     year = {2002},
     doi = {10.1051/cocv:2002064},
     zbl = {1044.93022},
     mrnumber = {1925038},
     language = {en},
     url = {}
AU  - Ilchmann, Achim
AU  - Ryan, E. P.
AU  - Sangwin, C. J.
TI  - Tracking with prescribed transient behaviour
JO  - ESAIM: Control, Optimisation and Calculus of Variations
PY  - 2002
DA  - 2002///
SP  - 471
EP  - 493
VL  - 7
PB  - EDP-Sciences
UR  -
UR  -
UR  -
UR  -
DO  - 10.1051/cocv:2002064
LA  - en
ID  - COCV_2002__7__471_0
ER  - 
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.

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