CAREER: Towards Scale-Invariant Identification and Synthesis Algorithms for Control Using Randomization

Networked systems such as smart city infrastructure and the Internet are engineering triumphs. However, modeling and designing controllers for systems of this scale is technically and computationally challenging at best, and intractable in the worst case. As the magnitude, complexity, and connectivity of these and future systems accelerates, so too do the technical challenges. Feedback control is the mechanism that enables engineers to guarantee desirable system behaviors such as stability (do the effects of disturbances decay over time?), performance (is the system operating efficiently?), and robustness (can performance and stability be maintained despite operating in an uncertain environment?). For networked systems, feedback control can only be applied in a distributed manner, there is no central decision maker. Unfortunately, distributed control is theoretically and computationally more challenging than its centralized counterpart. Moreover, distributed control requires transmission of potentially sensitive data over a network. Despite recent progress in distributed control and data privacy, there is a large gap between the complexity of systems we can control, and complexity of systems we want to control. The difference further increases when we additionally ask for data privacy guarantees. This project seeks to bridge the gap between theory, scalable computation, and data privacy and thus help make autonomous systems that we depend upon safe and trustworthy. Results from this research will enable the widespread adoption of distributed control in the aerospace, robotics, automotive, and energy industries.

This project consists of three foundational research topics; i) learning a dynamical system model from partially observed data, ii) designing robust and optimal distributed controllers from the model, and iii) integrating data privacy mechanisms into the modeling and control workflow. The contention of this research project is that it is impossible to achieve these goals for large-scale networked systems using traditional 'exact' methods. Instead we will formulate 'approximations' of the learning and control problems that can be solved at a fraction of the cost of doing so for the full problem. Correctly designed, these approximations can provide stability and performance guarantees for the original large-scale system. To achieve this formulation, we will develop new theory and algorithms based on randomized methods for numerical linear algebra and high-dimensional probability, customized for distributed control problems. Moreover, data privacy will be naturally accounted for as sensitive data gets compressed and transformed in the approximation stages.

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.