Controlled Synchronisation of Dynamical Systems Antonio Loria, Elena Panteley C.N.R.S., France loria@lss.supelec.fr panteley@lss.supelec.fr European Embedded Control Institute Graduate School –8th ed. Gif, Jan. 24-29 2011
SYNCHRONISATION ? Etymology: σ ´ υν –same; χρ ´ oνoς –time sharing the same time; occurring at the same time what occurs at the same time ? two processes; two phenomena; two events; two only? instantaneous events, phenomena, processes? REPETITIVE i.e. periodic? . . . RYTHM ( 2 / 10
RYTHM. . . Are the rythms and the events independent of each other or are they somehow connected ? Synchronisation is the adjustment of rythms of repetitive events (phenomena, processes) through weak interaction; the mutual time-conformity of two or more processes (events, phenomena) INTERACTION REPETITIVENESS RYTHM ( 3 / 10
Interaction, Repetitiveness, Rythm Repetition of a motion pattern; passes through a “point” (or infinitessimaly close to it) infinitely many times; depends only on its own parameters and dynamics (no external stimuli); does not depend on the initial conditions . . . ( 4 / 10
Interaction, Repetitiveness, Rythm Repetition of a motion pattern; passes through a “point” (or infinitessimaly close to it) infinitely many times; depends only on its own parameters and dynamics (no external stimuli); does not depend on the initial conditions . . . � �� � clocks . . . OSCILLATION COUPLING ( 5 / 10
Synchronization is . . . The interaction of rythms of oscillating objects due to their weak interaction interaction must occur through a weak coupling ; two synchronized oscillators must be separable into two self-sustained processes; adjustment is entailed and sustained through interaction; a small mismatch in the systems’ motions entails small variations in the synchronisation (stability) How does interaction takes place? What are the forms of coupling? can it be modified? ( 6 / 10
Examples of synchrony: Keywords neuron firing; Clock, Oscillator, flocks of migrating birds; Interaction, Cycle, banks of fish; fireflies; Repetitiveness, biological clocks ; Periodicity, Rythm, menstruation cycles ; Simultaneity, Stability, heart beating; Motion, Trajectory an orchestra . . . Coupling: cicardian rythm is connected with day/night and seasonal luminance variations; fireflies’ lightening is influenced by those of their neighbours; violonists hear the sound of their own violins and of others’ ( 7 / 10
Research aereas Physics Computer Science Nonlinear phenomena, Networks oscillations, chaos band allocation, clocks, . . . Biology SYNC enthomology, molecular biology, clocks, zoology, medicine Engineering Circuit theory Cooperative systems, van der Pol, Duffing, teleoperation, robotics L¨ u, Chen, Colpitts . . . formation control, Communications • UAVs, (sub)marine, • platooning, ( 8 / 10
Research aereas AUTOMATIC Physics Computer Science Nonlinear phenomena, CONTROL Networks oscillations, chaos band allocation, clocks, . . . Biology SYNC enthomology, molecular biology, clocks, zoology, medicine Engineering Circuit theory Cooperative systems, van der Pol, Duffing, teleoperation, robotics L¨ u, Chen, Colpitts . . . formation control, Communications • UAVs, (sub)marine, • platooning, ( 8 / 10
Classical examples Natural synchronization. Animals: fish, birds, fireflies, etc. Self synchronization ( 9 / 10
Classical examples Natural synchronization. Animals: fish, birds, fireflies, etc. Self synchronization Controlled . Master-slave (chaotic circuits) LORENZ LORENZ TRANSMITTER RECEIVER ( 9 / 10
Classical examples Natural synchronization. Animals: fish, birds, fireflies, etc. Self synchronization Controlled . Master-slave (chaotic circuits, teleoperation) LORENZ LORENZ TRANSMITTER RECEIVER ( 9 / 10
Classical examples Natural synchronization. Animals: fish, birds, fireflies, etc. Self synchronization Controlled . Master-slave Mutual – cooperative systems (satelittes, ships, vehicles’ formation) ( 9 / 10
Classical examples Natural synchronization. Animals: fish, birds, fireflies, etc. Self synchronization Controlled . Master-slave Mutual – cooperative systems (satelittes, ships, vehicles’ formation) Switched synchronisation ( 9 / 10
Classical examples Natural synchronization. Animals: fish, birds, fireflies, etc. Self synchronization Controlled . Master-slave Mutual – cooperative systems (satelittes, ships, vehicles’ formation) Switched synchronisation ( 9 / 10
Classical examples Natural synchronization. Animals: fish, birds, fireflies, etc. Self synchronization Controlled . Master-slave Mutual – cooperative systems (satelittes, ships, vehicles’ formation) Switched synchronisation ( 9 / 10
Lectures Outline Mutual synchronization; consensus graph theory (matrix theory), stability theory, basic algorithms; Synchronisation of Oscillators basic concepts, chaos , master-slave synchronization tracking, observer-based, Synchronisation of complex systems networks (pinning control) Kuramoto . . . Parkinson: a (de)synchronisation case-study ( 10 / 10
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