Abstract: Networked Chaotic Oscillators and Multi-Agent Cooperative Control: Common Strategies for Synchronization
The synchronization of phase and chaotic oscillators has certain common features with the problem of multi-agent cooperative control on compact manifolds such as SO(3), the configuration space of rigid body attitude, although these problems have historically been studied by researchers from separate disciplines (e.g. physics and engineering). Synchronization has been studied since 1665 when Christiaan Huygens observed that two pendulum clocks hung on a common beam would synchronize their swings to an opposing phase. The Kuramoto model, introduced in 1975, describes the synchronization of nonlinearly coupled oscillators, while the synchronization of chaotic oscillators, with a diverse set of applications including secure communications, neural, and ecological models, has been studied since 1983. The Master Stability Function (MSF), introduced in 1998 by Pecora and Carroll, is a commonly used tool in the physics literature to analyze the stability of synchronized states in networks of coupled chaotic oscillators. Recently, strategies have been proposed for achieving phase balancing (corresponding to a vanishing order parameter) in networked chaotic systems in addition to synchronization. On the other hand, the problem of multi-agent cooperative control with its diverse set of applications in robotics and autonomous systems is a major topic of research in the engineering and controls communities, although the majority of work focuses on systems with Euclidean configuration spaces. However, when 3D rotation matrices are used in a continuous linear consensus protocol to achieve rigid body attitude consensus on SO(3)^N (as in multi-spacecraft attitude synchronization) certain dynamical behavior can be observed that does not exist on Euclidean spaces, including both locally stable (e.g. balanced) and unstable nonconsensus equilibria.
This talk will explore the use of a common set of strategies, which are motivated by a study of the Kuramoto model, in both chaos synchronization (in which the MSF is employed to analyze the stability of the synchronized state) and in spacecraft attitude consensus control. Such strategies include the use of reshaping, time-varying coupling functions, and optimization of the network that governs the interactions between agents or individual oscillators. Simulations verify the applicability of these
strategies to both rigid body attitude consensus and chaos synchronization. Finally, the two areas are blended by applying the MSF approach to a set of chaotified rigid bodies in which the chaotically varying attitudes achieve consensus in both attitude and angular velocity.
Biographical Sketch
Eric A. Butcher is a Professor of Aerospace and Mechanical Engineering at the University of Arizona where he directs the Autonomous Space Vehicles and Astrodynamics Laboratory and has joint appointments with Electrical and Computer Engineering and the Applied Mathematics Graduate Interdisciplinary Program. He received the B.S. in engineering physics from the University of Oklahoma, M.S. and Ph.D. degrees in mechanical engineering from Auburn University, and a M.S. in aerospace engineering sciences from the University of Colorado. After obtaining his Ph.D. he was a postdoctoral fellow at Sandia National Laboratory, assistant and associate professor at the University of Alaska Fairbanks, and the Dwight and Aubrey Chapman Associate Professor at New Mexico State University prior to moving to the University of Arizona in 2014. A former associate editor of the Journal of Computational and Nonlinear Dynamics, the International Journal of Dynamics and Control, and The Journal of the Astronautical Sciences, his current research interests include stability and control of dynamic systems with time delay, parametric excitation, and fractional order derivatives; control and synchronization of chaotic systems; cooperative control of multi-agent systems; optimal orbital transfers and spacecraft GNC; and control of spacecraft relative motion and attitude with a focus on proximity operations and ISAM missions. His hobbies include hiking and mountain biking on Arizona trails.