Campus Event Calendar
Event Entry
What and Who
Automated Stability Proofs for Hybrid Systems using Lyapunov Functions
Jens Oehlerking
Avacs Virtual Seminar
AG 1, RG1
AG Audience
English
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Date, Time and Location
Friday, 23 March 2007
13:30
-- Not specified --
E1 4
024
Saarbrücken
Abstract
Stability is an important property of dynamical systems. A stable system
is resistant to temporary outside disturbances and will revover from
such disturbances on its own accord. For linear dynamical systems (i.e.,
systems that are defined by a single differential or difference
equation) exact methods for showing stability properties exist. These
methods can not be transferred to the domain of hybrid dynamical systems
-- in fact no complete method for proving stability of general hybrid
systems is known.
Therefore, alternative approaches for hybrid systems are needed. One of
the most promising concepts for showing stability of hybrid systems is
the Lyapunov function. A Lyapunov fuction is a generalized energy
function of the system. A Lyapunov function for a system maps each
possible system state onto a positive real number. Furthermore, along
every possible trajectory of the system, such a function must always be
strictly decreasing. Finding such a function can prove stability of a
hybrid system.
We deal with methods that can compute such functions automatically for a
given hybrid system. Starting from a parameterized function template
(quadratic functions), we use optimization techniques to find parameters
that result in a valid Lyapunov function. The constraints on such a
function can then be expressed as a matrix inequality, which can
efficiently be solved numerically.
is resistant to temporary outside disturbances and will revover from
such disturbances on its own accord. For linear dynamical systems (i.e.,
systems that are defined by a single differential or difference
equation) exact methods for showing stability properties exist. These
methods can not be transferred to the domain of hybrid dynamical systems
-- in fact no complete method for proving stability of general hybrid
systems is known.
Therefore, alternative approaches for hybrid systems are needed. One of
the most promising concepts for showing stability of hybrid systems is
the Lyapunov function. A Lyapunov fuction is a generalized energy
function of the system. A Lyapunov function for a system maps each
possible system state onto a positive real number. Furthermore, along
every possible trajectory of the system, such a function must always be
strictly decreasing. Finding such a function can prove stability of a
hybrid system.
We deal with methods that can compute such functions automatically for a
given hybrid system. Starting from a parameterized function template
(quadratic functions), we use optimization techniques to find parameters
that result in a valid Lyapunov function. The constraints on such a
function can then be expressed as a matrix inequality, which can
efficiently be solved numerically.
Contact
Roxane Wetzel
900
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Roxane Wetzel, 03/20/2007 13:57
Roxane Wetzel, 03/20/2007 13:53 -- Created document.
Roxane Wetzel, 03/20/2007 13:53 -- Created document.