When MIMO Control Meets MIMO Communication: A Majorization Condition for Networked Stabilizability

摘要

In this paper, we initiate the study of networked stabilization via a MIMOcommunication scheme between the controller and the plant. Specifically, thecommunication system is modeled as a MIMO transceiver, which consists of threeparts: an encoder, a MIMO channel, and a decoder. In the spirit of MIMOcommunication, the number of SISO subchannels in the transceiver is oftengreater than the number of data streams to be transmitted. Moreover, thesubchannel capacities are assumed to be fixed a priori. In this case, theencoder/decoder pair gives an additional design freedom on top of thecontroller, leading to a stabilization problem via coding/control co-design. Itturns out that how to take the best advantage of the coding mechanism is quitecrucial. From a demand/supply perspective, the design of the coding mechanismboils down to reshaping the demands for communication resource from differentcontrol inputs to match the given supplies. We study the problem for the caseof AWGN subchannels and fading subchannels, respectively. In both cases, wearrive at a unified necessary and sufficient condition on the capacities of thesubchannels under which the coding/control co-design problem is solvable. Thecondition is given in terms of a majorization type relation. As we go along,systematic procedures are also put forward to implement the coding/controlco-design. A numerical example is presented to illustrate our results.