Control-Theoretic Foundations for Trustworthy Generative Artificial Intelligence in Safety-Critical Engineering Systems

Generative artificial intelligence is increasingly used not only to create content but also to support decision-making in engineered systems, including robot motion planning, autonomous vehicles, and networked infrastructure. As these systems operate in the physical world, their decisions must satisfy strict safety requirements, coordinate reliably across multiple interacting components, and remain stable when operating in feedback with physical processes. Current generative artificial intelligence methods were not designed with these engineering requirements in mind, limiting their trustworthy deployment in safety-critical applications. The research supported by this award develops the mathematical foundations needed to make generative artificial intelligence safe, coordinated, and reliable for engineering systems. The research advances the national interest by enabling trustworthy artificial intelligence technologies that improve the safety and reliability of autonomous and networked systems while strengthening the scientific foundations of engineering decision-making in transportation, robotics, and infrastructure. The project will also train undergraduate and graduate students at the intersection of control engineering and machine learning, provide hands-on training through a multi-robot laboratory, and openly disseminate software, data, and educational materials with the research and education communities. This project establishes control-theoretic foundations for generative diffusion processes operating in constrained, distributed, and feedback-coupled settings. The research develops methods that certify the satisfaction of hard constraints throughout the generative sampling process, including techniques that account for reduced-order representations and uncertainty in the dynamics and constraints inferred from data. It further develops distributed protocols that allow multiple interacting generative systems to coordinate using only local communication while providing theoretical guarantees on convergence, training stability, and the influence of network structure on coordination quality. The project also establishes when a generative process can serve as a feedback policy for physical systems by characterizing the sensitivity of the generated decisions to the system state, the requirements for real-time implementation, and the conditions under which interconnected generative policies remain collectively stable. The research combines tools from control theory, including barrier certificates, sensitivity analysis, and interconnection theorems, with the mathematics of stochastic generative processes. The resulting theoretical contributions will be validated experimentally on a multi-robot testbed, connecting mathematical guarantees to measured performance on safety, coordination, and closed-loop tasks. 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.