Online Convex Optimization for Robust, High Precision Control

Regents Of The University Of Michigan - Ann Arbor, Ann Arbor MI

Investigators

Abstract

High precision control systems are crucial for numerous modern engineering applications such as hard disk drives, satellites, and photolithography systems. Challenges in high precision control include: (a) stringent performance requirements, (b) imperfect design models, and (c) unknown environmental disturbances. Existing control methods generally make optimistic assumptions about the disturbances acting on the system (e.g. completely random) or pessimistic assumptions (e.g. completely antagonistic). In contrast, recent online convex optimization methods aim to learn the disturbance characteristics and control the plant at the same time. However, model errors can cause catastrophic failures in such approaches and thus must be explicitly considered in the design and analysis. This research will explore the use of novel, robust online convex optimization methods to improve performance by using imperfect models to adapt the controller for specific disturbance features. The researched methods can lead to significant increases in the memory density of hard disk drives used for cloud storage. It can also improve satellite pointing accuracy leading to improved imaging for space science missions and higher data rates via optical communication. These outcomes will enhance the economic competitiveness of industries that rely on high precision control. The researchers technical approach merges tools from online convex optimization with robust control. This framework has recently achieved great success in sequential decision-making tasks. These methods use regret as a metric to balance between exploration and exploitation in the face of uncertainty. However, there is still a gap to make these approaches suitable for industrial control problems. This research focuses on bridging this gap for an important class of engineering problems, namely, robust disturbance rejection for high precision control systems. The research is divided into three thrusts. In Thrust 1, the fundamental performance limits for robust disturbance rejection under general settings will be developed. This will provide insight into cases that can benefit from more advanced nonlinear, time-varying controllers. In Thrust 2, novel versions of recursive least squares for robust disturbance rejection will be created. Recursive least squares and its variants are well studied online optimization algorithms. However, they can be sensitive to model errors when applied for disturbance rejection in certain feedback architectures. To address this, the researchers will create a new class of recursive least squares algorithms that are robust to such model uncertainty. Finally, Thrust 3 will focus on more general regret-based online convex optimization methods for robust disturbance rejection. These methods will also be validated via application to satellite line-of-sight control. 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.