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Drive-Based Motivation for Coordination of Limit Cycle Behaviors

Program in Applied Mathematics Brown Bag Seminar

Drive-Based Motivation for Coordination of Limit Cycle Behaviors
Series: Program in Applied Mathematics Brown Bag Seminar
Location: MATH 402
Presenter: Craig Thompson, Program in Applied Mathematics, University of Arizona

Constructing autonomous systems capable of high-level behaviors often involves reducing these behaviors to a collection of low-level tasks. This requires developing a method for switching among possible tasks. Recent work has developed continuous dynamical systems that have an internal drive state to select the desired task. In one particular result, authors considered a scenario where individual behaviors were encoded in control vector fields with unique, globally stable equilibria. A further level of complexity arises when one seeks to create a system that switches between tasks encoded as globally attracting sets with recurrent behaviors, rather than as point attractors. This presentation outlines the problem using the recently-developed drive-based dynamical framework. First we generalize the formulation of tasks as one part attracting set and one part recurrent behavior on said attracting set. Then as a proof-of-concept we demonstrate the existence of an attracting set consisting of orbits that repeatedly flow between two canonical limit cycles (e.g., Hopf oscillators). Finally we give some general results for the case of arbitrary disjoint limit cycles.