Algebraic Methods of Designing Spatially Distributed Control Systems and Their Approximations

Lehigh University, Bethlehem PA

Investigators

Abstract

Objective: In many engineered large-scale systems, automatic control implementations are still centralized, in the sense that the controller interfaces with the physical system at a fixed and relatively small number of actuators and sensors. However, recent technological advances have opened up new possibilities to change this picture by making the idea of micro devices with actuating, sensing, computing, and telecommunications capabilities feasible. Distributing a large array of such micro devices in a spatial configuration gives unprecedented capabilities for control that result in spatial distribution of the control variables in addition to the internal states of the underlying dynamical system. Important questions that arise are how to design controllers for these systems with regard to global objectives; how to determine the communication requirements in the controller array; and how can these control algorithms be implemented in a distributed fashion. The primary goal of this project is to develop some of the fundamental insights and tools that will allow us to exploit architectural properties of the underlying systems to design optimal controllers. Intellectual Merit: The proposed research will provide a novel approach to design and implementation of automatic control systems for spatially distributed systems. The main tool used in this research is the notion of spatial localization, approximation, and interpolation, which is established using spatial decay property of spatially distributed systems. The exploitation of spatial decay and development of approximation tools pose significant intellectual challenges. The research is based synthesis of new theoretical results in control, operator, and distributed optimization. Broader Impacts: This research program is highly relevant for optimal control of most spatially distributed systems. Successful completion of this research will provide necessary tools and components in facilitating the design and integration of distributed control systems on real platforms and fostering their adoption in various applications such as power networks, transportation networks, and biological systems. An integral part to this research program is an educational agenda involving K-12, undergraduate and graduate students with a broader impact of educating the next generation of engineers and researchers that are fluent in multidisciplinary research collaborations.