Formal Methods for Control of Nonlinear Systems

ISBN-13: 9780367219994 / Angielski / Twarda / 2022 / 272 str.

Jun Liu

Opis

While linear control is a well-established subject, analysis and design of nonlinear control systems remains a challenging topic due to some of the fundamental difficulties caused by nonlinearity. This book provides a unified computational approach to analysis and design of nonlinear systems.

Spis treści

1. Continuous-Time Dynamical Systems. 1.1. Continuous-Time Control System. 1.2. Existence of Local and Global Solutions. 1.3. Stability and Boundedness. 1.4. Safety and Reachability. 1.5. Control Lyapunov Functions. 1.6. Summary. 2. Discrete-Time Dynamical Systems. 2.1. Discrete-Time Control Systems. 2.2. Stability and Boundedness. 2.3. Safety and Reachability. 2.4. Summary. 3. Formal Specifications and Discrete Synthesis. 3.1. Transition Systems. 3.2. Linear-Time Properties. 3.3. Linear Temporal Logic. 3.4. ω-Regular Properties. 3.5. Formulation of Control Problems. 3.6. Discrete Synthesis. 3.7. Summary. 4. Interval Computation. 4.1. Interval Analysis 4.2. Interval Over-Approximations of One-Step Forward Reachable Sets of Discrete-Time Systems. 4.3. Interval Over-Approximations of One-Step Forward Reachable Sets of Continuous-Time Systems. 4.4. Interval Under-approximations of Controlled Predecessors of Discrete-Time Systems. 4.5. Interval Under-approximations of Controlled Predecessors of Continuous-Time Systems. 4.6. Summary. 5. Controller Synthesis via Finite Abstractions. 5.1. Control Abstractions. 5.2. Soundness. 5.3. Completeness via Robustness. 5.4. Extension to Continuous-Time Dynamical Systems. 5.5. Summary. 6. Specification-Guided Controller Synthesis via Direct Interval Computation. 6.1. Discrete-Time Dynamical Systems. 6.2. Properties of Controlled Predecessors. 6.3. Invariance Control. 6.4. Reachability Control. 6.5. Reach-and-Stay Control. 6.6. Temporal Logic Specifications. 6.7. Extension to Continuous-Time Dynamical Systems. 6.8. Complexity Analysis. 6.9. Summary. 7. Applications and Case Studies. 7.1. DC-DC Boost Converter. 7.2. Estimation of Domains-of-Attraction. 7.3. Control of the Moore-Greitzer Engine. 7.4. Mobile Robot Motion Planning. 7.5. Online Obstacle Avoidance. 7.6. Robotic Manipulator. 7.7. Bipedal Locomotion. 7.8. Summary.