Optimal control over unreliable networks with uncertain loss rates

In this work, we consider an optimal control problem for Networked Control Systems (NCS), where the loop is closed via an unreliable network. In order to inform the controller about the fates of the control packets, the actuator sends acknowledgements to the controller. In this work, different types of acknowledgements are considered. Since all packets are send over a network, we consequently assume, that all packets can get lost, i.e. the measurement packets, the control packets as well as the acknowledgement packets. The loss of these packets is modeled by independent and identically distributed (iid) Bernoulli processes. Finally, we assume that the parameters of these loss processes are not known exactly. Using this setup, we derive bounds for the uncertainty in the loss rates. Moreover, we present an algorithm to design a sub-optimal controller which can tolerate a given amount of network uncertainties.