Set Theory-Based Spacecraft Dynamics and Control

This book presents a unified set theory-based framework for spacecraft dynamics and control under multi-source uncertainties and data-sparse conditions. First, it develops reduced-order modeling techniques for high-dimensional spacecraft dynamics by introducing interval and convex set-based uncertainty descriptions, enabling efficient model reduction while rigorously quantifying unknown-but-bounded uncertainties without reliance on large-sample statistical assumptions. Second, the book addresses spacecraft attitude determination, attitude dynamics and control problems under uncertainty, establishing interval and convex set-based formulations for attitude dynamics and different control methods, including optimal control, sliding mode control, and periodic control, and systematically integrating non-probabilistic time-dependent reliability analysis into the dynamics and control design process to simultaneously account for performance and safety requirements. Finally, the proposed methodologies are extended to rigid–flexible coupling spacecraft, where attitude motion and structural vibration interact under uncertain conditions, and set theory-based spacecraft dynamics, optimal control and bounded model predictive control strategies are developed to achieve coordinated attitude–vibration suppression with guaranteed reliability and computational efficiency. Overall, the book provides a systematic methodology that links uncertainty dynamics, control synthesis, and reliability-based design optimization, offering both solid theoretical foundations and practical tools for the dynamics and control of advanced spacecraft operating in uncertain and data-limited environments.