A Control Lyapunov Perspective on Episodic Learning via Projection to State Stability
Andrew J. Taylor,Victor D. Dorobantu,Meera Krishnamoorthy,Hoang M. Le,Yisong Yue,Aaron D. Ames +5 more
- pp 1448-1455
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TLDR
In this paper, the authors employ Control Lyapunov Functions (CLFs) as low-dimensional projections to understand and characterize the uncertainty that these projected dynamics introduce in the system, and demonstrate that a practical episodic learning approach can use Projection to State Stability (PSS) to characterize uncertainty in the CLF.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.read more
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