Safety-Critical Controller Design for Nonlinear Systems: Stabilization and Robustness

This study proposes innovative closed-form solutions for designing safe controllers for nonlinear affine control systems, thereby eliminating the need for real-time quadratic programming optimization. We first focus on asymptotic stabilization using a Lyapunov-based control law, referred to as the “unsafe control", and introduce an additional state variable alongside a “safeguarding control" to guarantee safe operation of the closed-loop system. The proposed closed-form scheme limits the impact of the safeguarding control on the functionality of the closed-loop system, ensuring the derivative of a control Lyapunov function remains at least negative semi-definite. User-defined parameters provide flexibility in managing safety constraints, while the method s adaptability allows for integration with existing control techniques. Furthermore, we extend our results to robust safety control for nonlinear systems subject to external disturbances, ensuring both safety and input-to-state stability. In addition to theoretical developments, the effectiveness of the proposed controllers is validated through three comprehensive case studies, demonstrating their potential in real-world applications. The results highlight the controllers’ ability to maintain safety and stability without the computational burden of real-time quadratic programming, thereby enhancing their suitability for systems with fast dynamics. © 2025 Elsevier Ltd