Barrier States Theory for Safety-Critical Multi-Objective Control

TL;DR

This paper introduces a barrier states approach for integrating safety into multi-objective control systems, enabling safe stabilization and robust safety analysis using existing control methods.

Contribution

It presents a novel barrier states framework that embeds safety into control design, allowing legacy controllers to ensure safety and robustness in safety-critical systems.

Findings

Guarantees safe stabilization of original systems

Enables use of legacy control methods for safety

Introduces input-to-state safety (ISSf) and safe stability (IS3)

Abstract

Multi-objective safety-critical control entails a diligent design to avoid possibly conflicting scenarios and ensure safety. This paper addresses multi-objective safety-critical control through a novel approach utilizing barrier states (BaS) to integrate safety into control design. It introduces the concept of safety embedded systems, where the safety condition is integrated with barrier functions to characterize a dynamical subsystem that is incorporated into the original model for control design. This approach reformulates the control problem to focus on designing a control law for an unconstrained system, ensuring that the barrier state remains bounded while achieving other performance objectives. The paper demonstrates that designing a stabilizing controller for the safety embedded system guarantees the safe stabilization of the original safety-critical system, effectively mitigating conflicts between performance and safety constraints. This approach enables the use of various legacy control methods from the literature to develop safe control laws. Moreover, it explores how this method can be applied to enforce input constraints and extend traditional control techniques to incorporate safety considerations. Additionally, the paper introduces input-to-state safety (ISSf) through barrier states for analyzing robust safety under bounded input disturbances and develops the notion of input-to-state safe stability IS3 for analyzing and designing robustly safe stabilizing feedback controls. The proposed techniques and concepts are used in various examples including the design of proportional-integral-derivative-barrier (PIDB) control for adaptive cruise control.