Nader Sadegh

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 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">barrier states (BaS)</i> to integrate safety into control design. It introduces the concept of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">safety embedded systems</i>, 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<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{3}$</tex-math></inline-formula>) 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.

We present a Riccati-based framework for safety-critical nonlinear control that integrates the barrier states (BaS) methodology with the State-Dependent Riccati Equation (SDRE) approach. The BaS formulation embeds safety constraints into the system dynamics via auxiliary states, enabling safety to be treated as a control objective. To overcome the limited region of attraction in linear BaS controllers, we extend the framework to nonlinear systems using SDRE synthesis applied to the barrier-augmented dynamics and derive a matrix inequality condition that certifies forward invariance of a large region of attraction and guarantees asymptotic safe stabilization. The resulting controller is computed online via pointwise Riccati solutions. We validate the method on an unstable constrained system and cluttered quadrotor navigation tasks, demonstrating improved constraint handling, scalability, and robustness near safety boundaries. This framework offers a principled and computationally tractable solution for synthesizing nonlinear safe feedback in safety-critical environments.

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.