Uniformly hyperbolic control theory. (2017)

• Record Type: Journal Article
• Authors: Kawan, Christoph
• Is Part Of: Annual reviews in control. Volume 44(2017)
• Page Start: 89
• Page End: 96
• Publication Date: 2017
• Subjects: Control-affine system -- Uniform hyperbolicity -- Chain control set -- Controllability -- Robustness -- Networked control -- Invariance entropy; Automatic control -- Periodicals; Periodicals; 629.805
• DOI: 10.1016/j.arcontrol.2017.02.001
• Languages: English
• ISSNs: 1367-5788

Abstract

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.