Control without Trust: A Distributionally Robust Approach

ongoing

"Recent developments in sensing and communication technology offer unprecedented opportunities by ubiquitously collecting data at high detail and at large scale. Utilization of data at these scales, however, poses a major challenge for control systems, particularly in view of the additional inherent uncertainty that data-driven control signals introduce to systems behavior. In fact, this effect has not been well understood to this date, primarily due to the missing link between data analytics techniques in machine learning and the underlying physics of dynamical systems. I address this issue by proposing a novel control design paradigm embracing ideas from the emerging field of distributionally robust optimization (DRO). DRO is a decision-making model whose solutions are optimized against all distributions consistent with given prior information. Recent breakthrough work, among others by the PI of this proposal, has shown that many DRO models can be solved in polynomial time even when the corresponding stochastic models are intractable. DRO models also offer a more realistic account of uncertainty and mitigate the infamous ""post-decision disappointment"" of stochastic models. This proposal lays the theoretical foundation for distributionally robust control and aims to make progress along four directions. (i) Decision-dependent ambiguity: I introduce the concept of ""invariant ambiguity sets"" to encompass the dynamic evolution of uncertainty. (ii) Dynamic programming: I establish a dynamic programming characterization of the proposed DRO models and provide tractable approximation schemes along with rigorous theoretical bounds. (iii) Safe and memory-efficient learning: Leveraging modern tools from kernel methods and online-optimization, I propose tractable, yet provably reliable, synthesis tools. (iv) I plan to develop a tailor-made modeling language and open-source software to make distributionally robust control methods accessible in industry-size applications."