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CATEGORIES:CUED Control Group Seminars
SUMMARY:Control theory of switches and clocks - Rodolphe S
epulchre\, University of Cambridge
DTSTART;TZID=Europe/London:20180531T140000
DTEND;TZID=Europe/London:20180531T150000
UID:TALK106300AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/106300
DESCRIPTION:This talk will present a novel approach for the an
alysis and design of systems that switch and oscil
late. While such nonlinear behaviors abound in con
trol engineering of electrical\, mechanical\, and
biological circuits\, it is often considered that
they largely fall outside the scope of control the
ory. In contrast\, the proposed approach closely m
imics linear-quadratic dissipativity theory\, a ve
ry foundation of modern control theory.\n\nIn its
classical formulation\, dissipativity theory formu
lates system properties as dissipation inequalitie
s to be satisfied by the storage\, an abstraction
of the system internal energy. Linear systems admi
t quadratic storages. When the storage is positive
definite\, it serves as a Lyapunov function for s
tability analysis of equilibria. Our generalizatio
n rests on two distinct ingredients. First\, we ap
ply dissipativity theory differentially: instead o
f studying the nonlinear system via the nonlinear
theory\, we apply the linear theory to a family of
linearized systems. Second\, we relax the positiv
ity constraint of the quadratic storage to a fixed
inertia constraint. We allow for one negative eig
envalue in the analysis of switches and two negati
ve eigenvalues in the analysis of clocks.\n\nThe t
alk will illustrate the theory in classical models
of switches and clocks and discuss the potential
of dissipativity theory for the analysis and desig
n of interconnected systems away from equilibrium.
LOCATION:Cambridge University Engineering Department\, Lect
ure Room 5
CONTACT:Alberto Padoan
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