Lewis A.D. Tautological Control Systems

New York: Springer, 2014. — 128 p.This brief presents a description of a new modelling framework for nonlinear/geometric control theory. The framework is intended to be—and shown to be—feedback-invariant. As such, Tautological Control Systems provides a platform for understanding fundamental structural problems in geometric control theory. Part of the novelty of the text stems from the variety of regularity classes, e.g., Lipschitz, finitely differentiable, smooth, real analytic, with which it deals in a comprehensive and unified manner. The treatment of the important real analytic class especially reflects recent work on real analytic topologies by the author. Applied mathematicians interested in nonlinear and geometric control theory will find this brief of interest as a starting point for work in which feedback invariance is important. Graduate students working in control theory may also find Tautological Control Systems to be a stimulating starting point for their research.Introduction, Motivation, and Background
Topologies for Spaces of Vector Fields
Time-Varying Vector Fields and Control Systems
Presheaves and Sheaves of Sets of Vector Fields
Tautological Control Systems: Definitions and Fundamental Properties
Étalé Systems
Ongoing and Future Work