Inverse Optimal Safety Filters

TL;DR

This paper investigates the concept of infinite-horizon optimal safety filters for control systems, proposing new methods that extend beyond pointwise optimality to ensure long-term safety under disturbances.

Contribution

It introduces a framework for designing safety filters that are optimal over the entire infinite horizon, addressing limitations of existing pointwise QP safety filters.

Findings

Families of safety filters that guarantee infinite-horizon optimal safety.

Safety filters that degrade gracefully under unknown disturbances.

Illustrative examples demonstrating the effectiveness of the proposed filters.

Abstract

CBF-QP safety filters are pointwise minimizers of the control effort at a given state vector, i.e., myopically optimal at each time instant. But are they optimal over the entire infinite time horizon? What does it even mean for a controlled dynamic systems to be "optimally safe" as opposed to, conventionally "optimally stable"? When disturbances, deterministic and stochastic, have unknown upper bounds, how should safety be defined to allow a graceful degradation under disturbances? Can safety filters be designed to guarantee such weaker safety properties as well as the optimality of safety over the infinite time horizon? We pose and answer these questions for general systems affine in control and disturbances and illustrate the answers using several examples. In the process, using the existing QP safety filters, as well as more general safety-ensuring feedbacks, we generate entire families of safety filters which are optimal over the infinite horizon though they are conservative (favoring safety over `alertness') relative to the standard QP.