A tracking problem is considered in the context of a class of multi-input, multi-output, nonlinear systems modelled by controlled functional differential equations. The class contains, as a prototype, all finite-dimensional, linear, -input, -output, minimum-phase systems with sign-definite “high-frequency gain”. The first control objective is tracking of reference signals by the output of any system in : given , construct a feedback strategy which ensures that, for every (assumed bounded with essentially bounded derivative) and every system of class , the tracking error is such that, in the case , or, in the case , . The second objective is guaranteed output transient performance: the error is required to evolve within a prescribed performance funnel (determined by a function ). For suitably chosen functions , and , both objectives are achieved via a control structure of the form with , whilst maintaining boundedness of the control and gain functions and . In the case , the feedback strategy may be discontinuous: to accommodate this feature, a unifying framework of differential inclusions is adopted in the analysis of the general case .
Mots clés : functional differential inclusions, transient behaviour, approximate tracking, asymptotic tracking
@article{COCV_2009__15_4_745_0, author = {Ryan, Eugene P. and Sangwin, Chris J. and Townsend, Philip}, title = {Controlled functional differential equations : approximate and exact asymptotic tracking with prescribed transient performance}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {745--762}, publisher = {EDP-Sciences}, volume = {15}, number = {4}, year = {2009}, doi = {10.1051/cocv:2008045}, mrnumber = {2567243}, zbl = {1175.93188}, language = {en}, url = {http://www.numdam.org/articles/10.1051/cocv:2008045/} }
TY - JOUR AU - Ryan, Eugene P. AU - Sangwin, Chris J. AU - Townsend, Philip TI - Controlled functional differential equations : approximate and exact asymptotic tracking with prescribed transient performance JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2009 SP - 745 EP - 762 VL - 15 IS - 4 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/cocv:2008045/ DO - 10.1051/cocv:2008045 LA - en ID - COCV_2009__15_4_745_0 ER -
%0 Journal Article %A Ryan, Eugene P. %A Sangwin, Chris J. %A Townsend, Philip %T Controlled functional differential equations : approximate and exact asymptotic tracking with prescribed transient performance %J ESAIM: Control, Optimisation and Calculus of Variations %D 2009 %P 745-762 %V 15 %N 4 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/cocv:2008045/ %R 10.1051/cocv:2008045 %G en %F COCV_2009__15_4_745_0
Ryan, Eugene P.; Sangwin, Chris J.; Townsend, Philip. Controlled functional differential equations : approximate and exact asymptotic tracking with prescribed transient performance. ESAIM: Control, Optimisation and Calculus of Variations, Tome 15 (2009) no. 4, pp. 745-762. doi : 10.1051/cocv:2008045. http://www.numdam.org/articles/10.1051/cocv:2008045/
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