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DTSTART;TZID=Europe/Brussels:20221110T130000
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DTSTAMP:20260514T170632
CREATED:20221004T061444Z
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SUMMARY:Christian Mugisho Zagabe (University of Namur)
DESCRIPTION:Title: Lie-algebraic condition for uniform stability of switched nonlinear systems: Construction of a common Lyapunov function by the Koopman operator approach. \nAbstract: Switched systems consist of a finite set of dynamical systems and a switching signal indicating which system is activated. Their interest is due to the fact that many phenomena in nature\, engineering\,… are represented by different models depending on the change of some parameters. Their stability properties are not intuitive. Indeed\, for two individually stable (or unstable) systems one can construct a signal that makes the whole system unstable (or stable). In the uniform stability theory\, the main goal is to find sufficient (and/or necessary) conditions that make the whole system stable for all possible switching laws. \nIn 1999\, Daniel Liberzon and co-workers proved that for a switched linear system\, the solvability property of the Lie algebra generated by Hurwitz matrices is a sufficient condition for uniform stability. \nIn 2004\, Daniel Liberzon formulated an open problem to find which condition of the Lie algebra (of vector fields) can be used to guarantee the global uniform asymptotic stability (GUAS) of switched nonlinear systems.  \nUsing the Koopman operator approach\, we propose an answer to the open Liberzon problem. Our result is related to the dynamics on the polydisc and shows that a sufficient condition for GUAS follows from the solvability of the Lie algebra generated by the Hurwitz Jacobian matrices of the vector fields. \nMore precisely\, we construct a common Lyapunov function for switched nonlinear systems\, which is convergent in a specific region of the state space. This is done by defining the Koopman operator on the Hardy space on the polydisc where the reproducing kernel property allows us to obtain a Lyapunov function via the evolution of the evaluation functional. We then infer the GUAS property of switched nonlinear systems on a specific invariant set. \nThe seminar will take place in room S08 at the Faculty of Sciences
URL:https://www.naxys.be/event/christian-mugisho-zagabe-university-of-namur/
CATEGORIES:NAXYS Seminar
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DTSTART;TZID=Europe/Brussels:20221117T130000
DTEND;TZID=Europe/Brussels:20221117T140000
DTSTAMP:20260514T170632
CREATED:20221025T072145Z
LAST-MODIFIED:20221114T094213Z
UID:1719-1668690000-1668693600@www.naxys.be
SUMMARY:Ariane Courtot (IMCCE\, France)
DESCRIPTION:Title: Chaos in the Geminid Meteoroid stream \nAbstract: Meteor showers originate from a parent body (an asteroid or a comet). This parent body ejects several meteroids\, forming a meteoroid stream\, which will meet the Earth. From Earth\, several meteors can then be observed. To prove they actually form a shower\, we need to show whether they come from the same source. \nBut dynamically linking a meteor shower with its parent body can be challenging. This is in part due to the complex dynamics of meteoroid streams and the influence of non-gravitational forces (FNG). \nWe develop a method to study chaos in meteoroid streams and apply it to the Geminid meteoroid stream. We choose to draw chaos maps\, which relies on chaos indicator. We show that the best one is the Orthogonal Fast Lyapunov Indicator\, after comparison with the Fast Lyapunov Indicator\, the FLI for close encounters and the Mean Exponential Growth factor for Nearby Orbits. \nWe apply this method on the Geminids\, a well-known meteoroid stream. We show the influence of mean-motion resonances with the Earth and with Venus\, which tend to trap the largest particles. The chaos maps present 3 distinct regimes in eccentricity\, reflecting close encounters with the planets. We also study the effect of NGFs and we determine a first approximation of the particle size needed to counterbalance the resonances with the diffusion created by NGFs. \nThe seminar will take place in room S08 at the Faculty of Sciences
URL:https://www.naxys.be/event/ariane-courtot-institut-de-mecanique-celeste-et-de-calcul-des-ephemerides-imcce/
CATEGORIES:NAXYS Seminar
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