Keyou You

Background Mathematical Results

This chapter summarizes some basic concepts and results in linear algebra, probability theory, and stochastic processes, which are frequently utilized in the remaining chapters of this book. Most of the results are given without proof, except some very specific ones, whose derivations are neither straightforward nor extensively known. Detailed treatments of associated topics can be found in the references listed in the end of this chapter.

Distributed Control for Large-Scale NCSs

Recent years have witnessed an increasing attention on the study of distributed coordination for multiple agents due to its broad applications in many areas including formation control, distributed sensor network, flocking, distributed computation, and synchronization of coupled chaotic oscillators. A fundamental requirement on this topic is that all the agents should reach an agreement (consensus) using the shared data through local communications, which is determined by an underlying network topology. Toward this objective, a key step is to design a network-based control protocol such that as time goes on, all the agents asymptotically agree on some variable of interest in an appropriate sense. This chapter focuses on the problems of distributed control design for the consensus and formation of the discrete-time multiagent systems.

Control With Communication Constraints

Communication is an important component of networked control systems, and there is a need to understand the interactions between the control and communication components of the distributed system. In this chapter, we formulate a stabilization problem of linear systems over a communication channel that connects the sensor to the controller. Due to the communication data rate constraint, the information exchange between the sensor and controller has to be quantized before transmission. Quantization refers to the process of approximating the continuous set of values with a finite (preferably small) set of values. In fact, quantization has been a long research topic in communications and information theory; see [1] and the references therein. Here we are concerned with the quantized feedback control systems and focus on quantifying the minimum data rate for stabilization of linear systems.