Barrier States Theory for Safety-Critical Multiobjective Control

Multiobjective safety-critical control entails a diligent design to avoid possibly conflicting scenarios and ensure safety. This article addresses multiobjective safety-critical control through a novel approach utilizing barrier states 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. This article 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. In addition, this article introduces input-to-state safety through barrier states for analyzing robust safety under bounded input disturbances and develops the notion of input-to-state safe stability 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 control for adaptive cruise control.