Decentralized Local State Feedback Controller for Distributed Systems

Collaborators: Venkat Chandrasekaran, John Doyle,

This research project is an extension of a class project in collaboration with Yuh-Shyang Wang. In this project, we are interested in synthesizing a decentralized local state feedback controller for large scale distributed systems. To illustrate the goal of this project, consider the power grid across the United States. Suppose a blackout happens in New York. A good controller will ideally restrict the effect of the blackout within a small neighborhood around New York, and it will also ensure that the blackout only last for a finite amount of time. This localized closed loop effect implies that controllers far away, for example, Los Angeles and Chicago, do not need to know that New York has a blackout because it will not affect them. In other words, a good controller will ensure that a disturbance’s effect on a distributed system is finite in space and time. Therefore, each controller only needs to consider states within a small neighborhood around it and acts for a finite time. Such a controller is what we call a decentralized local state feedback controller. The figure shows a schematic of a distributed system with decentralized controller.

distributed_system

To numerically solve for a controller with above mentioned properties, we used nuclear norm approximation. For more details, please refer to our project report and presentation.