LQG Control For Distributed Systems Over TCP-like Erasure Channels

This paper is concerned with control applicationsover lossy data network. Sensor data is transmitted to anestimation-control unit over a network and control commandsare issued to subsystems over the same network. Sensor andcontrol packets may be randomly lost according to a Bernoulliprocess. In this context the discrete-time Linear QuadraticGaussian (LQG) optimal control problem is considered. In [1]a complete analysis was carried out for the case the networkis composed of a single sensor and control channel. Here anontrivial generalization to the case of sensor and actuatornetworks with p distinct sensor channels and m control channelsis presented. It has been proven that the separation principlestill holds for all protocols where packets are acknowledgedby the receiver (e.g. TCP-like protocols). Moreover it has beenpointed out for the first time that the optimal LQG control isa linear function of the state that explicitly depends on thecommand channels lost probabilities. Such a dependence isnot present in pre-existing literature, since the amplitude ofeach control input has to be weighted by the loss probabilityassociated to its own channel. This is not observed in the singlechannel case. In the infinite horizon case stability conditions onthe arrival are derived. Their computation requires the use ofLinear Matrix Inequalities (LMIs).