Meyer P. Interval Reachability Analysis...for Control and Verification 2021

Textbook in PDF format

This brief presents a suite of computationally efficient methods for bounding trajectories of dynamical systems with multi-dimensional intervals, or ‘boxes’. It explains the importance of bounding trajectories for evaluating the robustness of systems in the face of parametric uncertainty, and for verification or control synthesis problems with respect to safety and reachability properties. The methods presented make use of:
interval analysis;monotonicity theory;contraction theory; anddata-driven techniques that sample trajectories.
The methods are implemented in an accompanying open-source Toolbox for Interval Reachability Analysis.
This brief provides a tutorial description of each method, focusing on the requirements and trade-offs relevant to the user, requiring only basic background on dynamical systems. The second part of the brief describes applications of interval reachability analysis. This makesthe brief of interest to a wide range of academic researchers, graduate students, and practising engineers in the field of control and verification.
Preface
Acknowledgements
Introduction
Reachability Methods
Interval Analysis
Monotonicity
Mixed Monotonicity
Sampled-Data Mixed Monotonicity
Growth Bounds
Sampling-Based Methods
Applications
Safety and Reachability Verification
Measure of Robustness Against Parameter Uncertainty
Abstraction-Based Control Synthesis
Appendix A Obtaining Sign-Stability by Shifting a Bounded Variable
Appendix B TIRA Toolbox for Interval Reachability Analysis