Dr. Nikolai Matni
University of California, Berkeley
As the systems we build and the environments that they operate in become more complex, first-principle modeling becomes either impossible, impractical, or intractable, motivating the use of machine learning techniques for their control. As impressive as the empirical success of these methods appears to be on stylized test-cases, strong theoretical guarantees of performance, safety, or robustness are few and far between; however, such guarantees are essential when data-driven methods are applied to safety-critical systems or infrastructures. In the first part of this talk, we make concrete steps towards developing performance and stability guarantees in the data-driven setting by considering a classical problem from the optimal control literature, the Linear Quadratic Regulator (LQR), with the added twist that now the system dynamics are unknown. We provide, to the best of our knowledge, the first end-to-end baselines for learning and control in an LQR problem that do not require restrictive or unrealistic assumptions. A key technical tool used in deriving this result is our recently developed System Level Approach (SLA) to Controller Synthesis. The SLA provides a transparent connection between system structure, constraints, and uncertainty and their effects on controller synthesis, implementation, and performance — we exploit these properties to combine results from contemporary high-dimensional statistics and robust controller synthesis in a way that is amenable to non-asymptotic analysis. We then show how the solution to the “Learning-LQR” problem can be incorporated into an adaptive polynomial-time algorithm that achieves sub-linear regret. In the second part of this talk, we discuss how we can extend these ideas to large-scale data-driven autonomous systems, which encompass future incarnations of the smart-grid, intelligent transportation systems and software-defined networks. In this large-scale distributed setting, an additional challenge must be addressed: even when the system model is exactly known, designing robust systems with optimal performance guarantees is a challenging task. We show how the SLA allows for localized optimal controllers to be synthesized using convex programming, thus extending the performance and robustness guarantees of optimal/robust control, under mild and practically relevant assumptions, to systems of arbitrary size. We illustrate the usefulness of this approach with a frequency regulation problem in the power-grid, and show how it can be used to systematically explore tradeoffs in controller performance, robustness, and synthesis/implementation complexity. We conclude with our vision for a contemporary theory of autonomy and data-driven control, and outline ongoing efforts in extending the previous results to incorporate the guarantees of other learning and control paradigms, such as model predictive control and experiment design.
Published on April 5th, 2018
Last updated on April 4th, 2018