Vertical Contracts for Safety Control

TL;DR

This paper introduces a contract-based methodology to translate continuous-time safety control problems into discrete-time problems, enabling the use of efficient solution schemes for safety assurance.

Contribution

It formalizes safety control as contract implementation and develops a hierarchical approach to convert continuous-time problems into discrete-time ones.

Findings

Successfully characterizes continuous-time safety control via discrete-time solutions.

Provides a systematic method to construct control inputs for continuous-time safety.

Enables leveraging discrete-time solution schemes for continuous safety control.

Abstract

We propose a methodology that exploits the contract formalism to characterize the continuous-time safety control problem, which is often difficult to address, in terms of a discrete-time one, for which numerous efficient solution scheme exist. We construct contracts as pairs of assumptions and guarantees which are set-valued mappings that describe the safe boundaries within which the system must operate. By formalizing safety control as contract implementation, we develop a vertical hierarchy according to which we translate implementation from continuous to discrete time. We accomplish this by constructing a discrete-time system and a contract such that a solution to the continuous-time implementation problem can be characterized in terms of a solution to its discrete-time counterpart. We then use this characterization to construct a control input that establishes implementation in continuous time on the basis of the control sequence that achieves implementation in discrete time.