Abstract
We characterise aspects of our worlds (great and small) in formalisms that exhibit symmetry; indeed symmetry is seen as a fundamental aspect of any physical theory. These symmetries necessarily have an impact on the way systems exhibit reactive behaviour in a given world for a symmetry determines an equivalence between states making it appropriate for an reactive system to respond identically to equivalent states. We develop the concept of a General Transfer Function (GTF) considered as a building block for reactive systems, define the concept of full symmetry operator acting on a GTF, and show how such symmetries induce a quotient structure which simplifies the process of building an invertible domain model for control.
This work was supported in part by the NSF (CDA-9703217), by AFRL/IFTD (F30602-97-2-0032), and by DARPA/ITO/SDR DABT63-99-1-0022.
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Popplestone, R., Grupen, R.A. (2000). Symmetries in World Geometry and Adaptive System Behaviour. In: Sommer, G., Zeevi, Y.Y. (eds) Algebraic Frames for the Perception-Action Cycle. AFPAC 2000. Lecture Notes in Computer Science, vol 1888. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10722492_21
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DOI: https://doi.org/10.1007/10722492_21
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