Quantization and Coding for Decentralized LTI Systems

We study the communication rate requirements for centralized and decentralized control schemes when the plant and the controller are connected via a noiseless bandlimited channel. We introduce recursive quantizers that achieve monotonic boundedness and exponential stability of the worst-case state estimation error with minimum rate. Rate requirements for centralized schemes are shown to be lower than those for decentralized schemes. A quantification of the information sharing between the controllers, such as full, instant, and one-step delayed information sharing, is shown to crucial for communication requirements and complexity. Slepian-Wolf coding argument is used to show that information sharing by the controllers, and not by the plants, is sufficient to achieve the lower bound on the rate, and schemes confirming this efficiency are constructed. It is also shown that delay in communication between the controllers leads to higher rate requirements between the controllers and the plants.