Volume 15, Number 4, October-December 2009
|Page(s)||745 - 762|
|Published online||19 July 2008|
Controlled functional differential equations: approximate and exact asymptotic tracking with prescribed transient performance
Department of Mathematical Sciences, University
of Bath, Bath BA2 7AY, UK. firstname.lastname@example.org; email@example.com
2 School of Mathematics, University of Birmingham, Birmingham B15 2TT, UK. C.J.Sangwin@bham.ac.uk
Revised: 26 March 2008
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, 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 : given , construct a feedback strategy which ensures that, for every r (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 φ). For suitably chosen functions α, ν and θ, both objectives are achieved via a control structure of the form with , whilst maintaining boundedness of the control and gain functions u and k. 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 .
Mathematics Subject Classification: 93D15 / 93C30 / 34K20 / 34A60
Key words: Functional differential inclusions / transient behaviour / approximate tracking / asymptotic tracking
© EDP Sciences, SMAI, 2008
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