Robust and efficient quantization and coding for control of multidimensional linear systems under data rate constraints

Recently, we reported results on coding strategies for scalar feedback systems with data‐rate‐limited feedback channels in which the data‐rate constraints are time varying. Such rate‐varying channels are typically encountered in communication networks in which links between nodes are subject to noise, congestion, and intermittent disruption. The present paper describes results of extending this research into the multidimensional domain. An important consideration is that for systems of dimension greater than one, many classical feedback designs cannot be realized for operation near the theoretical minimum possible data rate. A novel control coding scheme will be presented, and in terms of this, it will be shown that the advantages of coarse signal quantization that had been reported earlier for scalar systems remain in the multidimensional case. The key is to allocate the communication bandwidth efficiently among faster and slower modes. We discuss various strategies that allocate bandwidth by scheduling the time slots assigned to each mode. In particular, we propose a ‘robust attention varying’ technique, whose merit will be discussed in terms of its robustness with respect to time‐varying communication channel capacity and also in terms of how well it operates when the feedback channel capacity is near the theoretical minimum data rate.