Consensus and Synchronization: From the Euclidean Space and the Circle to Lie Groups

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Seshan Chandrasekaran Ravi N. Banavar

Consensus and Synchronization

From the Euclidean Space and the Circle to Lie Groups

Seshan Chandrasekaran, Ravi N. Banavar, Arun D. Mahindrakar

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English

Society for Industrial & Applied Mathematics,U.S.
31 December 2025

Groups & group theory; Differential & Riemannian geometry; Applied mathematics; Non-linear science; Mathematical physics

Series: SIAM Spotlights

Coordination, consensus, and synchronization are found in diverse natural phenomena and engineering applications. Examples are flocking birds, illuminating fireflies, a school of fish, and distributed control and sensing. The simplest of such problems are set in the Euclidean spaces and the circle. Consensus and Synchronization: From the Euclidean Space and the Circle to Lie Groups moves beyond this domain to the more sophisticated setting of Lie groups with bi-invariant metrics and extends the mathematical theories of consensus and synchronization for generic scenarios. This is relevant to applications such as robotics, autonomous vehicles, and spacecraft.

By: Seshan Chandrasekaran, Ravi N. Banavar, Arun D. Mahindrakar
Imprint: Society for Industrial & Applied Mathematics,U.S.
Country of Publication: United States
ISBN: 9781611978797
ISBN 10: 1611978793
Series: SIAM Spotlights
Pages: 86
Publication Date: 31 December 2025
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

Rama Seshan Chandrasekaran is a project officer at the Robotics Research Centre, Department of Mechanical and Aerospace Engineering, Nanyang Technological University Singapore. His research interests include differential geometry, topology, geometric physics and Lie Groups. He was a finalist for the Best Student Paper award at the European Control Conference in 2022. Ravi N Banavar is institute chair professor in systems and control engineering at the Indian Institute of Technology Bombay. He had a brief teaching stint at UCLA (1991–1992) before joining the systems and control engineering group at IIT Bombay. His research interests are in the field of geometric mechanics and nonlinear and optimal control with applications to electromechanical and aerospace engineering problems. He is an associate editor of Systems and Control Letters, on the editorial advisory board of the International Journal of Control, and a technical associate editor of the IEEE Control Systems Society Magazine. Arun D Mahindrakar is a professor in the department of electrical engineering at the Indian Institute of Technology Madras. He was a Postdoctoral Fellow with the Laboratory of Signals and Systems, Supelec in Paris from 2004 to 2005. His research interests include nonlinear stability, geometric control, formation control of multi-agent systems, and convex optimization.