A Control Lyapunov Perspective on Episodic Learning via Projection to State Stability
Abstract
The goal of this paper is to understand the impact of learning on control synthesis from a Lyapunov function perspective. In particular, rather than consider uncertainties in the full system dynamics, we employ Control Lyapunov Functions (CLFs) as low-dimensional projections. To understand and characterize the uncertainty that these projected dynamics introduce in the system, we introduce a new notion: Projection to State Stability (PSS). PSS can be viewed as a variant of Input to State Stability defined on projected dynamics, and enables characterizing robustness of a CLF with respect to the data used to learn system uncertainties. We use PSS to bound uncertainty in affine control, and demonstrate that a practical episodic learning approach can use PSS to characterize uncertainty in the CLF for robust control synthesis.
Keywords
Cite
@article{arxiv.1903.07214,
title = {A Control Lyapunov Perspective on Episodic Learning via Projection to State Stability},
author = {Andrew J. Taylor and Victor D. Dorobantu and Meera Krishnamoorthy and Hoang M. Le and Yisong Yue and Aaron D. Ames},
journal= {arXiv preprint arXiv:1903.07214},
year = {2020}
}