A Control Lyapunov Perspective on Episodic Learning via Projection to State Stability
This work addresses control synthesis under uncertainty for robotics or autonomous systems, but it appears incremental as it builds on existing Lyapunov and stability concepts.
The paper tackles the problem of understanding how learning affects control synthesis by introducing Projection to State Stability (PSS), a new notion that characterizes uncertainty in projected dynamics using Control Lyapunov Functions, and demonstrates its application for robust control synthesis in episodic learning.
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.