  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 (IS$^3$) 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.
