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.

A tracking problem is considered in the context of a class 𝒮 of multi-input, multi-output, nonlinear systems modelled by controlled functional differential equations. The class contains, as a prototype, all finite-dimensional, linear, m-input, m-output, minimum-phase systems with sign-definite “high-frequency gain”. The first control objective is tracking of reference signals r by the output y of any system in 𝒮: given λ0, construct a feedback strategy which ensures that, for every r (assumed bounded with essentially bounded derivative) and every system of class 𝒮, the tracking error e=y-r is such that, in the case λ>0, lim sup t e(t)<λ or, in the case λ=0, lim t e(t)=0. The second objective is guaranteed output transient performance: the error is required to evolve within a prescribed performance funnel ϕ (determined by a function ϕ). For suitably chosen functions α, ν and θ, both objectives are achieved via a control structure of the form u(t)=-ν(k(t))θ(e(t)) with k(t)=α(ϕ(t)e(t)), whilst maintaining boundedness of the control and gain functions u and k. In the case λ=0, 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 λ0.

DOI : https://doi.org/10.1051/cocv:2008045
Classification : 93D15,  93C30,  34K20,  34A60
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},
     zbl = {1175.93188},
     mrnumber = {2567243},
     language = {en},
     url = {http://www.numdam.org/item/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/item/COCV_2009__15_4_745_0/

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