Learning Safety Filters for Unknown Discrete-Time Linear Systems
This work addresses safety-critical control for unknown systems, which is incremental as it builds on existing constraint-tightening methods by incorporating learning and adaptation.
The paper tackles the problem of ensuring safety for discrete-time linear systems with unknown models and noise by developing a learning-based safety filter that minimally modifies control actions to satisfy polytopic constraints with high probability, achieving this through robust optimization with constraint tightening that adapts over time as data accumulates.
A learning-based safety filter is developed for discrete-time linear time-invariant systems with unknown models subject to Gaussian noises with unknown covariance. Safety is characterized using polytopic constraints on the states and control inputs. The empirically learned model and process noise covariance with their confidence bounds are used to construct a robust optimization problem for minimally modifying nominal control actions to ensure safety with high probability. The optimization problem relies on tightening the original safety constraints. The magnitude of the tightening is larger at the beginning since there is little information to construct reliable models, but shrinks with time as more data becomes available.