LQG control for MIMO systems over multiple erasure channels with perfect acknowledgment

This technical note concerns control applications over lossy data networks. Sensor data is transmitted to an estimation-control unit over a network and control commands are issued to subsystems over the same network. Sensor and control packets may be randomly lost according to a Bernoulli process. In this context, the discrete-time linear quadratic gaussian (LQG) optimal control problem is considered. In Schenato , a complete analysis was carried out for the case that sensor measurements and control inputs are delivered into a single packet to the estimator and to the actuators respectively. Here, a nontrivial generalization for MIMO systems is presented under the assumption that each sensor and each actuator exchange data with the control unit in an independent way by using their own data packet (no aggregation). In such a framework, it is shown that the separation principle still holds in the case where packet arrivals are acknowledged by the receiver. Moreover, the optimal LQG control is a linear function of the state that explicitly depends on the loss probabilities of the actuator channels. Such a dependence is not present in the single channel case considered in mean-square. In the infinite horizon case, stability conditions on the packet arrival probabilities are provided in terms of linear matrix inequalities (LMIs).