Safety-Critical Control with Lyapunov and Barrier Functions

This book integrates stability via Lyapunov functions and safety enforcement via barrier functions for nonsmooth dynamics. It bridges theory with real-time implementation for autonomous vehicles, robotics, and energy networks. Ideal for graduate students, researchers, and practitioners in control systems requiring safety-critical methods. This book presents a comprehensive framework for designing control systems that must operate safely in complex, real-world environments. It addresses the critical challenge facing modern autonomous systems: how to guarantee both stability and safety when dynamics are inherently nonsmooth. Safety-Critical Control with Lyapunov and Barrier Functions: From Smooth to Nonsmooth Methods presents a unified methodology integrating stability (via Lyapunov functions) and safety constraint enforcement (via barrier functions). Its key strength is the rigorous treatment of nonsmooth dynamics using generalized derivatives, set-valued mappings, and differential inclusions. The text progresses systematically from nonsmooth analysis and stability theory through safety enforcement and unified synthesis methods, including optimization-based quadratic program controllers and Lyapunov-barrier function designs. It bridges abstract theory with real-time implementation, addressing practical constraints such as input saturation and dynamic environments. Readers gain theoretical understanding and practical tools to design control systems for autonomous vehicles, robotics, energy networks, and other safety-critical applications requiring simultaneous performance and constraint satisfaction. This book is designed for graduate students, researchers, and practitioners in control systems engineering, robotics, autonomous systems, and applied mathematics who…