Tautological Control Systems

This brief presents a description of a new modelling framework for nonlinear/geometric control theory. The framework is intended to beand shown to befeedback-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.

Promises a new methodology of study with fundamentally novel tools leading to a radically different way of understanding system structure Eliminates the need to consider control parameterization and the effects of its variation New approach will inspire further work and discussion Includes supplementary material: sn.pub/extras

Auteur
Professor Lewis has worked in the areas of geometric mechanics and geometric control theory, lately the latter more so than the former. He is a recognised expert in geometric control theory. He has written many papers on geometric control theory and geometric mechanics, and has supervised five doctoral theses in these areas. He is the author of Geometric Control of Mechanical Systems, published by Springer and dealing with the interface of his two areas of expertise. Together with Manuel de Leon and Juan-Pablo Ortega, Professor Lewis started the Journal of Geometric Mechanics as a venue for publishing research in these areas.

Contenu

1 Introduction, motivation, and background.- 2 Topologies for spaces of vector fields.- 3 Time-varying vector fields and control systems.- 4 Presheaves and sheaves of sets of vector fields.- 5 Tautological control systems: Definitions and fundamental properties.- 6 Étalé systems.- 7 Ongoing and future work.