Scalable Decision-making for Autonomous Systems in Space Missions
Author: Changhuang Wan
Publisher:
Published: 2021
Total Pages: 0
ISBN-13:
DOWNLOAD EBOOKTimely and well-based decision-making plays a crucial role in improving the performance, success rate, and safety of autonomous aerospace systems, especially for those involving multi-agent networks, hybrid dynamical systems, and operations under uncertain environments. Many space missions benefit from the performance and resilience improvements that employing optimal decision-making strategies significantly increases autonomy level, maneuverability, and multi-task capability. However, in real-world applications, a wide range of aerospace systems involve decisions at different autonomy levels and they are usually coupled with each other, which makes it challenging to find the optimal mixed-variable decisions. Optimization and optimal control are the main tools in decision-making. This dissertation aims to develop a systemic rank-constrained optimization methodology for the decision-making of autonomous systems in space missions where the system states are represented by mixed discrete and continuous variables. Rank constrained optimization is to optimize a convex function subject to a convex set of constraints and a rank constraint on the unknown matrix. It has received increasing attention in the areas of matrix completion, signal processing, and model reduction, just to name a few. However, the connection between rank-constrained optimization, especially for rank one-constrained optimization, and mixed-variable decision-making problems has not been well established. In fact, any discrete variable can be regarded as a continuous variable with a polynomial equality constraint. Meanwhile, many system dynamics can be converted into polynomial constraints through discretization and conversion of expressions. Thus, a mixed-variable decision-making problem could be cast as a polynomial optimization problem, which can be expressed as an equivalent quadratically constrained quadratic programming (QCQP) problem by introducing extra variables and quadratic equalities. Furthermore, a general QCQP can be equivalently transformed into a linear matrix programming problem by introducing a to-be-determined rank-one matrix. This dissertation focuses on establishing computationally efficient programs to solve the resulting rank constrained optimization problems and to evaluate the effectivity, efficiency, and performance of the proposed methodologies in decision-making for autonomous systems stemming from applications closely related to space missions. The products contain (1) development of a unified modeling route to formulate a decision-making problem to a general QCQP or rank-constrained optimization problems (RCOP), (2) proposition of four different sequential algorithms, named alternating minimization algorithm (AMA) combined with penalty function, Alternating Projection Approach (APA), Alternating Rank Minimization Approach (ARMA), and Customized Alternating Direction Method of Multipliers (ADMM), to solve the resulting QCQP or RCOP, (3) applications in space missions including a mission planning for spacecraft rendezvous and docking mission, and a fuel optimal guidance for Mars entry, powered descent, and landing mission, (4) applications in other areas including a sensor localization mission of a multi-agent system, and a UAV path-planning problem. Work in this dissertation removes a computational bottleneck in solving a broad class of challenging mixed-variable optimization problems using a uniform formulation associated with a standard routine. The research products, composed of theoretical analysis, algorithm developments, and practical applications, collectively contribute to the full autonomy of a wide class of autonomous systems in space missions.