Collaborative Research: CPS-FR: A Control-Theoretic Framework for Reliable and Robust Deep Neural Networks with Application to Space CPS

This collaborative research project aims to advance the current state-of-the-art in space autonomy. While deep learning algorithms have transformed many terrestrial applications, including autonomous driving and humanoid robotics, similar advances have not yet been fully realized for space-borne platforms. In close collaboration with the Space Vehicles Directorate of the Air Force Research Lab (AFRL), this project promotes the integration of learning-enabled components, including deep neural networks, on board a spacecraft to achieve levels of trusted space autonomy to support future space missions. A major obstacle in materializing this vision is the current inability to certify these learning-enabled components (LEC) in continuous operation. To overcome this obstacle, this project proposes a transformational paradigm shift by treating deep neural network (DNN) training as a feedback control design problem. Leveraging optimal and robust control theory techniques will allow to effectively address major challenges such as uncertainty and noise in DNNs, as well as reason about stability, expressiveness, and robustness. The broader impacts of the project include training both graduate and undergraduate students, disseminating the results to the scientific community via journal and conference publications, organizing invited workshops and seminar presentations, and reaching the broader public through targeted engagement with popular media, including press releases and interviews. The key innovation of the proposed approach is the formulation of DNN training as a distributional control problem, which allows leveraging powerful tools from dynamical systems and control theory to answer difficult questions regarding constraint satisfaction and efficient DNN training with guarantees. The project brings together three PIs with technical expertise in stochastic and nonlinear control, stability theory, convex optimization, and training of large-scale DNNs to tackle the foundational challenges of designing safe learning-enabled systems (LES). The proposed approach consists of three key ingredients. First, it introduces methods for propagating distributions through neural networks via characteristic functions, branch-and-bound optimization techniques, and scenario-based optimization, thereby enabling probabilistic verification of ReLU-based neural networks. Second, it develops principled methodologies for designing DNNs that provide robustness guarantees against disturbance inputs, leading to faster, more reliable DNN training while ensuring satisfaction of safety constraints. Third, it proposes designing globally optimal controllers within a convex model class using Clifford algebra ideas, yielding computationally tractable controllers with probabilistic safety guarantees. The proposed theoretical framework can be used not only to train DNN and fine-tune pre-trained DNNs to satisfy safety constraints, but also to come up with new DNN architectures. Together, these three ingredients are evaluated under a rigorous plan of increasing complexity and realism, starting with high-fidelity simulations in a synthetic environment, followed by hardware experiments at Georgia Tech, and finally by experimental validation on larger platforms at the Space Vehicles Directorate of AFRL. Although this project is motivated by, and has a direct impact on, spacecraft applications, the same theory and mathematical techniques have much broader relevance to a wide range of CPS that employ DNNs as their core learning mechanism. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.