Uniformly hyperbolic control theory

TL;DR

This paper explores the application of uniform hyperbolicity concepts from smooth dynamical systems to control-affine systems, revealing new insights into controllability, robustness, and stabilizability.

Contribution

It introduces a novel transfer of hyperbolic theory to control systems, combining geometric control and dynamical systems theories for non-local control results.

Findings

Results on controllability in hyperbolic control systems

Robustness properties derived from hyperbolic dynamics

Practical stabilizability in networked control frameworks

Abstract

This paper gives a summary of a body of work at the intersection of control theory and smooth nonlinear dynamics. The main idea is to transfer the concept of uniform hyperbolicity, central to the theory of smooth dynamical systems, to control-affine systems. Combining the strength of geometric control theory and the hyperbolic theory of dynamical systems, it is possible to deduce control-theoretic results of non-local nature that reveal remarkable analogies to the classical hyperbolic theory of dynamical systems. This includes results on controllability, robustness, and practical stabilizability in a networked control framework.