LQG control for systems with random unbounded communication delay

In this paper LQG control over unreliable communication links is examined. That is to say, the communication channels between the controller and the actuators and between the sensors and the controller are unreliable. This is of growing importance as networked control systems and use of wireless communication in control are becoming increasingly common. A proposed approach is to use tree codes to turn lossy channels into ones with a random delay. The problem of how to optimize LQG control in this case is examined, and it is found that to optimize LQG control previous control signals must also be used. Only the situation where communication between the components is done with acknowledgments is examined. An optimal solution is derived for finite horizon discrete hold-input LQG control for this case. The solution is compared with standard LQG control in simulations, which demonstrate that a significant improvement in the cost can be achieved when the probability of delay is high.