Feedback control over limited capacity channels

In this chapter, we present recent approaches towards networked control systems (NCSs) motivated by capacity constraints in communication channels. Consideration of such constraints is important since the channels are shared by various system components, and thus the communication rate necessary for control-related signals must be explicitly taken into account. The chapter consists of two main parts. In the first part, we discuss control problems involving quantization effects. While such problems have a long history in the control field, the characteristic aspect here is that the problems have strong ties to the theoretical question on how much information is necessary for the purpose of feedback control. The second part provides an information theoretic approach to the well-known Bode's integral formulae, where properties of sensitivity functions are characterized by the plant poles and zeros. We will observe the usefulness of notions such as entropy in deriving such formulae. The results in both parts exhibit fundamental limitations that arise due to the presence of capacity limited channels and are hence unique to networked control. Moreover, we will describe the close interplay between the two fields of control and communication. © 2010 Springer London.