Grant: Discovery Grants Program - Individual

Background: Accurate position and orientation control of spacecraft with flexible structures, such as tethers, solar panels, and booms, is crucial for mission success. This typically requires experts who have undergone extensive training and possess specialized expertise in control. One wonders if it is possible to algorithmically synthesize stable feedback laws to control such spacecraft's coupled rigid-flexible dynamic behavior or, more broadly, dynamic systems with infinite degrees of freedom, analogous to how the finite element method (FEM) solves physical problems in modern engineering. Currently, we find no answer to this question in control. Research Program: The proposed research is to fill this gap in control by developing a novel computational control framework. This framework can numerically synthesize stable feedback laws by algorithms analogous to the FEM process. Then, it integrates the feedback laws seamlessly into the FEM program to empower engineers to execute nonlinear feedback control for coupled rigid-flexible dynamic systems in multi-physical domains without extensive control expertise. Over the next five years, three focused short-term objectives, blending theory, simulations, and experiments, will drive breakthroughs in two cutting-edge areas. This first is a new approach to multi-fidelity multi-physics modeling for coupled rigid-flexible spacecraft dynamics. It proposes a physics-informed multilayer neural network to surrogate computation-intensive high-fidelity components while retaining the high-fidelity of the rest in the model. The resulting model is both computation-efficient and accurate, intended to replace the continuous dynamic system with infinite degrees of freedom by a discrete system model for computational control development. The second breaks new ground in computational control by using FEM in spatial space to approximate the stabilizing feedback control law for dynamic systems with infinite degrees of freedom, unlike traditional methods that replace the control laws with piecewise ones in state space. It will allow engineers to control coupled rigid-flexible dynamic systems with numerical control laws, similar to solving engineering problems with FEM. Significance: The ambition to algorithmically automate the synthesis of stabilizing feedback laws is transformative. It represents a pivotal shift analogous to how FEM transformed the engineering field. Theoretically, success in this work could lead to a new research direction in computational control. It signifies not just an incremental advancement but potentially a foundational leap that could establish new study areas in control engineering. Practically, it promises engineers advanced tools for streamlined control design and optimal performance. In addition, the proposed research will train the next generation of HQP needed to meet the increasing needs of industry for both fundamental scientific discovery and innovations in industrial applications.