Graduation Semester and Year
Spring 2026
Language
English
Document Type
Dissertation
Degree Name
Doctor of Philosophy in Aerospace Engineering
Department
Mechanical and Aerospace Engineering
First Advisor
Dr. Kamesh Subbarao
Abstract
Modern mechanical and aerospace systems increasingly operate autonomously in environments characterized by nonlinear dynamics, uncertainty, and safety constraints. In these settings, estimation and control methods based on nominal models and single-point trajectory predictions are usually insufficient to ensure safe and reliable operation. This dissertation uses a set-theoretic perspective, in which the system state, uncertainty, and admissible behavior are described by sets instead of point estimates. The key question is not only what the state is, but what set of states remains consistent with the dynamics, disturbances, control limits, and available measurements. This provides bounded descriptions of uncertainty and supports control laws with formal guarantees under unknown-but-bounded disturbances and modeling errors.
The dissertation develops an integrated framework built on set-theoretic reachability analysis, set-membership state estimation, and Model Predictive Control (MPC). The first part focuses on reachable-set computation for nonlinear systems using zonotopes and constrained zonotopes. A Taylor-series-based propagation framework with bounded linearization error is developed to compute outer and inner approximations in the presence of state and input constraints. These ideas are applied to hypersonic atmospheric re-entry, where safe reachable tubes are used as constraints within linear time-varying, nonlinear, and tube-based MPC formulations. The framework is then extended to low-thrust spacecraft in two-body and cislunar environments using both direct nonlinear Taylor expansion and state-dependent coefficient parameterization, facilitating reachability-informed station-keeping about cislunar periodic orbits.
The second part addresses estimation and control under bounded uncertainty for spacecraft rendezvous and proximity operations. Ellipsoidal and zonotopic set-membership filters are integrated with MPC for linear time-varying relative dynamics. A hybrid zonotopic set-membership Kalman filter is then developed for 6-DOF proximity operations in the presence of mixed stochastic and unknown-but-bounded uncertainty. The method bounds the Lagrange linearization remainder using zonotopes, derives a gain that accounts for both stochastic covariance and set-valued uncertainty, and provides state estimates for MPC-based trajectory guidance.
The final part extends MPC to cooperative robotic systems, including multi-rover lunar exploration under communication and terrain constraints, aerial-ground docking of a micro aerial vehicle on a mobile platform, and real-time quadrotor trajectory tracking with online zonotopic safe-corridor enforcement. Together, these developments show that set-theoretic reachability and set-membership estimation complement predictive control by enabling uncertainty-aware estimation and safety-critical control for mechanical and aerospace systems.
Keywords
Set-theoretic reachability; Model predictive control; Zonotopes; Set-membership filtering; Robust control; Spacecraft proximity operations
Disciplines
Aerospace Engineering | Astrodynamics | Mechanical Engineering | Navigation, Guidance, Control and Dynamics | Space Vehicles
License
This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 International License.
Recommended Citation
Patel, Jinaykumar Nitinkumar, "Set-theoretic Reachability-informed Model Predictive Control for Mechanical and Aerospace Systems" (2026). Mechanical and Aerospace Engineering Dissertations. 3.
https://mavmatrix.uta.edu/mechaerospace_dissertations2/3
Included in
Astrodynamics Commons, Mechanical Engineering Commons, Navigation, Guidance, Control and Dynamics Commons, Space Vehicles Commons
Comments
Degree granted by The University of Texas at Arlington