This project advances the theory and methods underlying the development of computationally lightweight control algorithms that ensure the safe and reliable operation of autonomous systems in safety-critical applications. Such methods can benefit a broad range of industrial uses, including autonomous drone delivery, robotics, manufacturing, aerial and ground transportation, autonomous driving, and precision agriculture. To fully realize their benefits, autonomous systems must be capable of making reliable decisions in real time while operating in complex environments with rapidly changing constraints. This is especially challenging because modern autonomous systems are often designed to reduce cost, weight, and energy consumption, which limits their onboard computing capabilities. To address these challenges, this project pursues a systematic and theoretically justified framework, grounded in extensions to Control Barrier Function (CBF) methods, that enables the design of control algorithms ensuring the satisfaction of safety constraints even when computational resources are severely limited. Control Barrier Functions (CBFs) hold significant promise for addressing constrained control challenges in nonlinear systems and for providing computationally lightweight solutions that ensure the safety and reliable operation of autonomous systems. At the same time, systematic design procedures for CBFs are currently limited to specific classes of systems and constraints. To provid