CAREER: Hybrid Control of Complex Networked Systems

Stanford University, Stanford CA

Investigators

Abstract

This project is devoted to research and teaching in the area of hybrid systems theory. The goal is to develop a control theory for complex networks of systems, each with its own objectives, decision-making, and information processing capabilities. The systems have dynamics which are primarily continuous-state and continuous-time, yet the aggregate network is in general too complex to model with continuous tools alone. Control theory to date has achieved tremendous success in the analysis and synthesis of single control systems, as well as the development of control laws for groups of systems which are connected together by point-to-point links so that information is received and processed synchronously at each subsystem. Using continuous-state tools, simple hierarchical control schemes have also been designed and used with great success. The control of an aircraft is an excellent example: the complex system of hydraulic valves which controls the surfaces of today's commercial jets is transparent to the pilot, due to a control layer in between that bounds the operation of the hydraulics and displays this simplified abstraction of the complex system to the pilot. We are now interested in designing control laws for systems which are vastly more complex than continuous, synchronous control theory allows. Examples include air traffic control systems, highway systems, communication systems, the interconnected power grid, financial networks such as the stock market, and networks of distributed MEMS sensors. In each of these examples, the sensors and resources are distributed across the systems, yet there is a strong need for the systems to coordinate to perform some task or achieve some goal. The systems are also asynchronous, since correlated but different information is available to the controllers at different times. We propose to design hierarchical, hybrid control systems: ours will be a hierarchy in which discrete state models are used at the highest level to model the large mode spaces in the system, and in which the lowest level incorporates distributed sensing and control, asynchronous receipt and processing of information, and multiple objective functions. Our research will focus on: 1. Design of the real-time hybrid interface: A key focus of this research is on the development of a robust and computationally efficient hybrid system interface between the discrete-state system abstraction and the continuous-state subsystems. This interface will provide a priori proofs that the system will function as desired, and automatic synthesis of both discrete and continuous control laws. 2. Control of asynchronous systems: Hand-in-hand with autonomous interacting agents comes the issue of asynchrony. In classical control theory, sensor data is sampled and actuator commands are issued at a fixed rate. We propose to design an asynchronous control theory, in which sensors transmit time-stamped data packets whenever new information is available and controllers pick up packets relevant to their current function. 3. Algorithms for automated air traffic systems: In future air transportation systems, it is proposed to automate and move much of the current air traffic control functionality on board the aircraft. This provides a superb environment in which to develop the theory proposed here, and we will draw on this rich application domain for examples and laboratory experiments. The education component of this project is a new curriculum in control theory at Stanford. The courses will combine systems theory from both control theoretic and computer science perspectives. In addition, a new Laboratory will be developed, with the goal of studying, modeling, and controlling complex systems.