Logics and Proof Calculi for Hybrid Systems -- Differential Dynamic Logic d? -- Differential-Algebraic Dynamic Logic DAL -- Differential Temporal Dynamic Logic dTL -- Automated Theorem Proving for Hybrid Systems -- Deduction Modulo Real Algebra and Computer Algebra -- Computing Differential Invariants as Fixed Points -- Case Studies and Applications in Hybrid Systems Verification -- European Train Control System -- Air Traffic Collision Avoidance -- Conclusion.

Hybrid systems are models for complex physical systems and have become a widely used concept for understanding their behavior. Many applications are safety-critical, including car, railway, and air traffic control, robotics, physical–chemical process control, and biomedical devices. Hybrid systems analysis studies how we can build computerized controllers for physical systems which are guaranteed to meet their design goals. The author gives a unique, logic-based perspective on hybrid systems analysis. It is the first book that leverages the power of logic for hybrid systems. The author develops a coherent logical approach for systematic hybrid systems analysis, covering its theory, practice, and applications. It is further shown how the developed verification techniques can be used to study air traffic and railway control systems. This book is intended for researchers, postgraduates, and professionals who are interested in hybrid systems analysis, cyberphysical or embedded systems design, logic and theorem proving, or transportation and automation.