Analysis of Regulation Problems based on Real-Time Rate-Distortion Theory

This paper treats the relations between regulation and information in single agent control problems. We establish a-priori bounds for the attainable regulation accuracy in scalar and in multivariable control problems which result from the limited flow of information to the controller and the "variety" of the controlled outputs. In the analysis of the effect of a limited flow of information on the regulation accuracy, the real-time rate-distortion theory developped by Gorbunov and Pinsker is used. We discuss the tightness of the bounds and show that in special cases they define the optimal performance.