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CATEGORIES:CUED Control Group Seminars
SUMMARY:Controllability and stabilizability of piecewise a
ffine dynamical systems - Kanat Camlibel\, Univers
ity of Groningen
DTSTART;TZID=Europe/London:20161110T140000
DTEND;TZID=Europe/London:20161110T150000
UID:TALK68249AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/68249
DESCRIPTION:Being one of the most fundamental concepts of syst
ems and control theory\, the controllability conce
pt has been extensively studied\, ever since conce
ived by Kalman\, in various contexts including lin
ear systems\, nonlinear systems\, infinite-dimensi
onal systems\, positive systems\, switching system
s\, hybrid systems\, and behavioral systems. Easil
y verifiable tests for global controllability have
been hard to obtain with the exception of the cla
ssical results on finite-dimensional linear system
s. In fact\, even in the framework of smooth nonli
near systems\, results on controllability are loca
l in nature and there is no hope to come up with g
eneral algebraic characterizations of global contr
ollability. Indeed\, the problem of characterizing
controllability for some classes of systems fall
into the most undesirable category of problems fro
m computational complexity point of view\, namely
undecidable problems. A remarkable example of such
system classes is the so-called sign-systems whic
h are the simplest instances of piecewise affine d
ynamical systems.\n\nA piecewise affine dynamical
system is a finite-dimensional nonlinear input/sta
te/output dynamical system with the distinguishing
feature that the functions representing the syste
ms differential equations are piecewise affine fun
ctions. Any piecewise affine system can be conside
red as a collection of ordinary finite-dimensional
linear input/state/output systems\, together with
a partition of the product of the state space and
input space into polyhedral regions. Each of thes
e regions is associated with one particular linear
system from the collection. Depending on the regi
on in which the state and input vector are contain
ed at a certain time\, the dynamics is governed by
the linear system associated with that region. Th
us\, the dynamics switches if the state-input vect
or changes from one polyhedral region to another.
Any piecewise affine systems is therefore also a h
ybrid system\, i.e.\, a dynamical system whose tim
e evolution is governed both by continuous as well
as discrete dynamics.\n\nIn this talk\, we invest
igate controllability and stabilizability conditio
ns for continuous piecewise affine dynamical syste
ms. Although every piecewise affine system is a no
nlinear system\, none of the existing results for
smooth nonlinear systems can be applied to piecewi
se affine systems because of the lack of smoothnes
s. The main results of this talk are algebraic nec
essary and sufficient conditions for controllabili
ty and stabilizability of continuous piecewise aff
ine systems. These conditions are much akin to cla
ssical Popov-Belevitch-Hautus controllability/stab
ilizability conditions.
LOCATION:Cambridge University Engineering Department\, LR4
CONTACT:Tim Hughes
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