Computational Methods for Large-scale Interconnected Systems with Continuous and Discrete Parameters
Abstract
This project is motivated by the computational challenges arising in the control of many complex real-world systems such as communication networks, electrical power systems, aerospace systems, large-space flexible structures, traffic systems, wireless sensor networks, and various multi-agent systems. The objective is to study the distributed control of the slow time-scale behavior of an interconnected system, modeled by nonlinear algebraic equations having some underlying structure that captures the physical architecture of the system. The goal is to address operational problems such as resource allocation, state estimation and topology control, using efficient distributed algorithms that are able to handle non-convexity and stochasticity by exploiting the structure of the system. Our technical approach relies on conic optimization, convex relaxation, algebraic geometry, penalization techniques, and distributed computation, among others. To achieve the goals of this project, we will address the following objectives: (1) design of an efficient mathematical framework to find a global or near-global solution (with a guaranteed optimality guarantee) for optimization problems associated with the operation of a given interconnected system, (2) optimal estimation of the unknown state of an interconnected system in presence of noisy data and conflicting information, (3) study of non-convex robust decision-making problems and stochastic optimization for interconnected systems, (4) co-optimization of the topology of a given interconnected system to achieve a higher performance by exploiting the embedded flexibility, (5) design of distributed computation techniques for the developed mathematical frameworks, (6) implementation of the designed algorithms in a high-performance solver, and (7) testing of the efficacy of the designed tools and techniques on various real-world distributed systems, particularly those with DoD applications. This proposed project is highly interdisciplinary and combines convex analysis, nonlinear optimization, graph theory, matrix completion, stochastic control, and low-rank optimization. The outcome of this project would be efficient computational methods for the control and operation of large-scale distributed systems. This project would have a major impact on Applied Mathematics and Engineering by significantly advancing the areas of complex networks, control theory, and optimization. The techniques to be developed in this project can be exploited to address a broad set of highly structured nonlinear optimization problems.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Sep 11, 2018
- Source ID
- W911NF1710555
Entities
People
- Shmuel Oren
Organizations
- Army Contracting Command
- United States Army
- University of California, Berkeley