The Geometry of Hybrid Dynamical Systems- From Intrinsic Properties to Robust Hybrid Geometric Control
Abstract
Many control problems are difficult to solve due to topological obstructions that are intrinsic to the system being controlled. Such obstructions emerge in most autonomous vehicles problems. In particular, achieving robust global asymptotic stability of the attitude of a rigid body is rife with topological difficulty stemming from the very structure of the rigid body state space, which, unavoidable, includes the special orthogonal group of order three (SO(3)). Although geometric controllers can be designed to avoid singularities associated with a local chart, designing a smooth global controller on a compact manifold or a compact Lie group is nontrivial. Fortunately, it is possible to achieve global and robust asymptotic stability using hybrid feedback controllers. However, most hybrid control algorithms in the literature embed the ambient manifold (or space) in Euclidean space, namely, they rely on coordinates. In fact, the design of hybrid controllers that are geometric - in the sense that they are coordinate free - has not been explored much, with only a few special cases of manifolds treated thus far. Arguably, one reason for such lack of development is perhaps the fact that most theories for the study of hybrid dynamical systems focus on hybrid systems written on specific coordinates. In this project, we propose to fill this gap by generating tools that exploit the natural dynamics and geometry of the system to be controlled, and lead to i) methods for the study of geometry and intrinsic properties of hybrid dynamical systems, given rise to a new framework that we refer to as geometric hybrid dynamical systems, and ii) tools for the design of geometric hybrid control algorithms assuring that the desired properties hold with robustness to uncertainty.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Feb 29, 2024
- Source ID
- FA95502310313
Entities
People
- Ricardo G. Sanfelice
Organizations
- Air Force Office of Scientific Research
- United States Air Force
- University of California, Santa Cruz