Safety Assurance Framework for Pre-Designed Controllers: Control Barrier Function-based Safety Filters

1. Introduction Control systems in safety-critical domains must operate within strict constraints, yet conventional pre-designed controllers such as PID controllers are difficult to modify once deployed and offer no formal guarantees. This work introduces a safety assurance framework that augments such controllers with a Control Barrier Function-based safety filter. The approach is demonstrated on two representative systems showing that it can enforce safety without altering the existing controller structure. 2. CBF-based Safety Filters The aim of the safety filter is to smoothly adjust the control signal generated by the existing controller, with minimal intervention, as the system approaches the boundary of the safety set [1]. The standard nonlinear affine control system: The safe set 𝐶be defined by the 𝐵(𝑥) : 𝐵(𝑥) is a CBF for the system on the safe set 𝐶[2], if there exist a class 𝕂-function 𝛼(⋅) such that for any 𝑥: The terms as 𝐿𝑓𝐵(𝑥) = 𝜕𝐵(𝑥) 𝜕𝑥 𝑓(𝑥) and 𝐿𝑔𝐵(𝑥) = 𝜕𝐵(𝑥) 𝜕𝑥 𝑔(𝑥) [3]. The inequality constraints derived by the CBFs in quadratic form [2,4]: 3. Applications 3.1 Electromechanical Ball-and-Beam System Figure 1: The ball-and-beam system with electromechanical subsystem. The system is characterized by the following state variables: The safe set: 3.2 Anesthesia Control System An example for biomedical control domain: The time-varying safety set for the induction phase of anesthesia: Figure 4: Effect-site concentration responses under PID and CBF+PID control. The CBF: The relative degree 2 inequality condition : Figure 2: The portrait of states 𝑥1and 𝑥3with the unsafe region. The CBF: The time-varying inequality condition [6] : Figure 5: The corresponding BIS outputs. 4. Conclusion The results demonstrate that, in both examples, CBFs successfully ensure the safety. In the ball-and-beam system, the ball position and beam angle remain within the safe region, while in the anesthesia system, patients stay within the safety boundaries across the population models. The safety filter intervenes by modifying the input but gradually converges to the nominal controller inputs. However, the overall control performance is reduced under the safety filter operation, reflecting the inherent trade-off between safety and control performance. Safety Assurance Framework for Pre-Designed Controllers: Control Barrier Function-based Safety Filters DYNAMICAL SYSTEMS AND CONTROL RESEARCH GROUP Student: Bora Ayvaz Promoters: Dr. Dana Copot, Prof. Clara M. Ionescu Contact [email protected] www.ugent.be Universiteit Gent @ugent Ghent University References [1] Wabersich, K. P., Taylor, A. J., Choi, J. J., Sreenath, K., Tomlin, C. J., Ames, A. D., & Zeilinger, M. N. (2023). Data-driven safety filters: Hamilton-jacobi reachability, control barrier functions, and predictive methods for uncertain systems. IEEE Control Systems Magazine, 43(5), 137-177. [2] Ames, A. D., Xu, X., Grizzle, J. W., & Tabuada, P. (2016). Control barrier function based quadratic programs for safety critical systems. IEEE Transactions on Automatic Control , 62 (8), 3861-3876. [3] Wieland, P., & Allgöwer, F. (2007). Constructive safety using control barrier functions. IFAC Proceedings Volumes, 40(12), 462-467. [4] Nguyen, Q., & Sreenath, K. (2016, July). Exponential control barrier functions for enforcing high relative-degree safety-critical constraints. In 2016 American Control Conference (ACC) (pp. 322-328). IEEE. [5] Ionescu, C. M., Neckebroek, M., Ghita, M., & Copot, D. (2021). An open source patient simulator for design and evaluation of computer based multiple drug dosing control for anesthetic and hemodynamic variables. IEEE Access, 9, 8680-8694. [6] Wang, H., Peng, J., Zhang, F., Zhang, H., & Wang, Y. (2022). High-order control barrier functions-based impedance control of a robotic manipulator with time-varying output constraints. ISA transactions, 129, 361-369. Figure 3: Anesthesia control system with CBF-based safety filter [5].