Universal tracking control is investigated in the context of a class of -input, -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 -valued reference signal of class (absolutely continuous and bounded with essentially bounded derivative) and every system of class , the tracking error between plant output and reference signal evolves within a prespecified performance envelope or funnel in the sense that for all , where a prescribed real-valued function of class with the property that for all and . A simple (neither adaptive nor dynamic) error feedback control of the form is introduced which achieves the objective whilst maintaining boundedness of the control and of the scalar gain .
Classification : 93D15, 93C30, 34K20
Mots clés : nonlinear systems, functional differential equations, feedback control, tracking, transient behaviour
@article{COCV_2002__7__471_0, 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 = {http://www.numdam.org/articles/10.1051/cocv:2002064/} }
TY - JOUR 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 - http://www.numdam.org/articles/10.1051/cocv:2002064/ UR - https://zbmath.org/?q=an%3A1044.93022 UR - https://www.ams.org/mathscinet-getitem?mr=1925038 UR - https://doi.org/10.1051/cocv:2002064 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. http://www.numdam.org/articles/10.1051/cocv:2002064/
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