Hybrid dynamical systems as coalgebras

Abstract: Lyapunov theory provides a method for certifying the stability of a dynamical system without solving infeasible systems of differential equations. This theory has practical implications in the design of control algorithms for many sorts of systems including robotics. We present a categorical framework for Lyapunov stability theory. This theory is developed in the language of coalgebras, where a system is viewed as a coalgebra of an endofunctor. Examples include continuous dynamical systems as coalgebras of the tangent bundle functor, and discrete transition systems as coalgebras of the powerset functor. We blend these two standard examples to give a coalgebraic encoding of hybrid dynamical systems, which appear naturally in engineering contexts such as robotic bipedal locomotion. This enables us to apply the categorical Lyapunov theory to hybrid systems and find new conditions for certifying the stability of Zeno equilibria.

algebraic topologycategory theory

Audience: researchers in the topic

Bilkent Topology Seminar

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