Minimax control over unreliable communication channels

In this paper, we consider a minimax control problem for linear time-invariant (LTI) systems over unreliable communication channels. This can be viewed as an extension of the H∞ optimal control problem, where the transmission from the plant output sensors to the controller, and from the controller to the plant are over sporadically failing channels. We consider two different scenarios for unreliable communication. The first one is where the communication channel provides perfect acknowledgments of successful transmissions of control packets through a clean reverse channel, that is the TCP (Transmission Control Protocol). Under this setting, we obtain a class of output feedback minimax controllers; we identify a set of explicit threshold-type existence conditions in terms of the H∞ disturbance attenuation parameter and the packet loss rates that guarantee stability and performance of the closed-loop system. The second scenario is one where there is no acknowledgment of successful transmissions of control packets, that is the UDP (User Datagram Protocol). We consider a special case of this problem where there is no measurement noise in the transmission from the sensors. For this problem, we obtain a class of corresponding minimax controllers by characterizing a set of (different) existence conditions. We also discuss stability and performance of the closed-loop system. We provide simulations to illustrate the results in all cases.