Tracking with prescribed transient behaviour

Ilchmann, Achim, Ryan, E. P., and Sangwin, C. J.. "Tracking with prescribed transient behaviour." ESAIM: Control, Optimisation and Calculus of Variations 7 (2002): 471-493. <http://eudml.org/doc/245146>.

@article{Ilchmann2002,
abstract = {Universal tracking control is investigated in the context of a class $\{\mathcal \{S\}\}$ 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 $\mathbb \{R\}^M$-valued reference signal $r$ of class $W^\{1,\infty \}$ (absolutely continuous and bounded with essentially bounded derivative) and every system of class $\{\mathcal \{S\}\}$, the tracking error $e$ between plant output and reference signal evolves within a prespecified performance envelope or funnel in the sense that $\{\varphi \}(t)\Vert e(t)\Vert &lt; 1$ for all $t\ge 0$, where $\{\varphi \}$ a prescribed real-valued function of class $W^\{1,\infty \}$ with the property that $\{\varphi \}(s)&gt;0$ for all $s &gt; 0$ and $\liminf _\{s\rightarrow \infty \}\{\varphi \}(s)&gt;0$. A simple (neither adaptive nor dynamic) error feedback control of the form $u(t)=- \alpha (\{\varphi \}(t)\Vert e(t)\Vert )e(t)$ is introduced which achieves the objective whilst maintaining boundedness of the control and of the scalar gain $\alpha (\{\varphi \}(\cdot )\Vert e(\cdot )\Vert )$.},
author = {Ilchmann, Achim, Ryan, E. P., Sangwin, C. J.},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {nonlinear systems; functional differential equations; feedback control; tracking; transient behaviour; time-varying feedback control; tracking funnel control; reference signals; performance funnel; nonlinear delay system; systems with hysteresis; relay hysteresis; backlash hysteresis; asymptotic stabilization; simulations; constant gain feedback; adaptive -tracking; universal tracking; memory; disturbance; nonlinear causal operator},
language = {eng},
pages = {471-493},
publisher = {EDP-Sciences},
title = {Tracking with prescribed transient behaviour},
url = {http://eudml.org/doc/245146},
volume = {7},
year = {2002},
}

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
PB - EDP-Sciences
VL - 7
SP - 471
EP - 493
AB - Universal tracking control is investigated in the context of a class ${\mathcal {S}}$ 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 $\mathbb {R}^M$-valued reference signal $r$ of class $W^{1,\infty }$ (absolutely continuous and bounded with essentially bounded derivative) and every system of class ${\mathcal {S}}$, the tracking error $e$ between plant output and reference signal evolves within a prespecified performance envelope or funnel in the sense that ${\varphi }(t)\Vert e(t)\Vert &lt; 1$ for all $t\ge 0$, where ${\varphi }$ a prescribed real-valued function of class $W^{1,\infty }$ with the property that ${\varphi }(s)&gt;0$ for all $s &gt; 0$ and $\liminf _{s\rightarrow \infty }{\varphi }(s)&gt;0$. A simple (neither adaptive nor dynamic) error feedback control of the form $u(t)=- \alpha ({\varphi }(t)\Vert e(t)\Vert )e(t)$ is introduced which achieves the objective whilst maintaining boundedness of the control and of the scalar gain $\alpha ({\varphi }(\cdot )\Vert e(\cdot )\Vert )$.
LA - eng
KW - nonlinear systems; functional differential equations; feedback control; tracking; transient behaviour; time-varying feedback control; tracking funnel control; reference signals; performance funnel; nonlinear delay system; systems with hysteresis; relay hysteresis; backlash hysteresis; asymptotic stabilization; simulations; constant gain feedback; adaptive -tracking; universal tracking; memory; disturbance; nonlinear causal operator
UR - http://eudml.org/doc/245146
ER -