| Abstract: |
| We establish a version of Conley`s Fundamental Theorem [1] for a
recently proposed category of hybrid dynamical systems [2] designed to
support a physically grounded type theory for specifying and
implementing reactive steady state and transitional robotic behaviors.
After reviewing some motivating ideas, the talk will outline a proof
that every object in an appropriately constrained subcategory of [2]
admits a global Lyapunov function in the sense of Conley [1]. We
briefly consider the gap between this subcategory and a larger class
of robotics-focused hybrid dynamical models from which it is inspired.
We close with some speculative remarks bearing on the future prospects
for a synthetic theory wherein for each compositional operation in the
category there is a corresponding operation on scalar valued functions
such that the composition of Lyapunov functions is a Lyapunov function
for the composition of the constituent objects.
References
[1] C. C. Conley, Isolated invariant sets and the Morse index. Amer
Mathematical Society, 1978.
[2] J. Culbertson, P. Gustafson, D. E. Koditschek, and P. F. Stiller, Formal composition of hybrid systems, ArXiv191101267 Cs Math, Nov. 2019. |
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