High-Performance Techniques for Optimal Distributed Control
Abstract
This project is motivated by the computational challenges arising in the control of many complex real-world systems such as communication networks, aerospace systems, large-space flexible structures, traffic systems, wireless sensor networks, and various multi-agent systems. The objective is to design an optimal distributed controller for a large-scale system with complete or incomplete infonnation about the model in an uncertain environment. This problem, even in the special detenninistic case, amounts to a non-convex optimization problem that is difficult to solve and remains an open problem after 50 years of study. This project aims to develop a new mathematical foundation for the design of optimal distributed controllers, which can be applied to a wide range of real-world complex networks. Local search methods are at the core of large-scale computation for machine learning problems and in particular reinforcement learning techniques via deep neural networks. These numerical methods are based on iteratively improving an existing control policy via computing some gradient and updating the parameters. In this project, we investigate the usefulness of local search for solving the optimal distributed control (ODC) problem and design a set of one-shot and sequential local search methods for solving ODC either precisely or approximately (depending on how difficult the instance of the ODC problem is). To this end, we first study the topological properties of the feasible set of the ODC problem for systems with known models, i.e., the set of all stabilizing distributed controllers ( or control policies). We analyze how many disjoint (connected) components this set has and how non-convex each component is. We study how the structural properties of the system as well as the communication architecture of the controller affect the topological properties ofODC. Using this analysis, we characterize how hard each sub-class of ODC problems is, how many communication channels are indeed among the local controllers to make the problem tractable, and how to design local search algorithms to find the best controller possible. Our mathematical framework combines local search with a homotopy technique to avoid becoming stuck at poor local (sub-optimal) solutions. For systems with incomplete knowledge about the model, we use reinforcement learning and first study how local search for policy update affects the perfonnance and then design better learning techniques for finding a near-globally optimal distributed controller in this setting. We perfonn case studies on real-world systems with DoD applications (such as control of a network of autonomous agents to cooperatively perfonn a task). The proposed approach is highly interdisciplinary and combines control theory, non-convex analysis, algebraic geometry, homotopy, graph theory, machine learning, and numerical methods. The outcome of this project is a set of efficient computational methods for the synthesis of large-scale complex networks and their associated communication architectures. This project has a major impact on Applied Mathematics and Engineering by significantly advancing the areas of complex networks, control theory, and nonlinear optimization.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Jul 09, 2020
- Source ID
- W911NF2010219
Entities
People
- Javad Lavaei
Organizations
- Army Contracting Command
- United States Army
- University of California, Berkeley