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.

References in corpus (2)

• Neural Lander: Stable Drone Landing Control using Learned Dynamics
• Episodic Learning with Control Lyapunov Functions for Uncertain Robotic Systems

Cited by in corpus (3)

• Bayesian Learning-Based Adaptive Control for Safety Critical Systems
• A Control Barrier Perspective on Episodic Learning via Projection-to-State Safety
• Neural Identification for Control