Stabilization with Finite Data Rates

In this term project, we study the effects of finite communication rates in control problems. Traditionally, the communication channel between the plant and the controller is not modelled. This is because it is assumed that the outputs of the former (noisy or noiseless) are available completely and with infinite precision to the latter. In this work, we study systems where the link between the plant and the controller can carry only a limited number of data symbols per unit time. We refer to these as systems with finite data rate. We consider three different systems in the order of increasing complexity. The first [1] is a scalar, linear time varying system with finite data rate. The conditions under which this system is asymptotically stabilizable are studied. The second system [2] is a finite dimensional, linear time invariant system. The exponential stabilizability of this system under a data rate constraint is studied. Finally, we consider the most general case a finite dimensional, linear system with both process and observation noise [3]. We find conditions that the data rate should satisfy in order to ensure mean square state stability of this system. Before we proceed, a word about the notation used. We use upper case letter to denote random variables, lower-case ones to denote their realizations. A sequence [x0, x1, . . . , xk] is denoted xk. Matrices and vectors are denoted using bold font.