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.