Suboptimal Safety‐Critical Control of Nonlinear Systems With Time‐Varying Constraints

ABSTRACT This paper develops a suboptimal safety‐critical control framework for nonlinear systems subject to time‐varying constraints by integrating barrier‐state augmentation with the state‐dependent Riccati equation (SDRE) technique. First, a single‐barrier design guarantees asymptotic stabilization and forward invariance of slowly evolving safe sets. Next, a multibarrier extension assigns each safety constraint its own barrier state and weighting factor, enabling independent tuning of conservativeness. At each time step, the controller solves a pointwise SDRE for the augmented dynamics. We establish that, provided the employed state‐dependent coefficient (SDC) representation is pointwise controllable and observable, the origin of the closed‐loop system remains asymptotically stable as long as the variation rates of the safety constraints are bounded. A key extension addresses scenarios where safety constraints and stabilization objectives are in conflict, ensuring forward invariance of time‐varying safe sets even when the origin may belong to the unsafe set. To this end, we introduce a conflict‐resolution barrier state and a discounted cost formulation that prioritizes safety over stability until constraints realign. Simulation results on mobile‐robot collision avoidance and quadrotor navigation tasks show strict enforcement of time‐varying constraints, successful handling of conflicts, and up to 50% faster computation than standard CBF‐QP methods, demonstrating the real‐time viability of the proposed method for complex safety‐critical applications.