Biblio

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.

Abstract— This paper considers a minimax control (H^∞) control) problem for linear time-invariant (LTI) systems where the communication loop is subject to a TCP-like packet drop network. The problem is formulated within the zero-sum dynamic game framework. The packet drop network is governed by two independent Bernoulli processes that model control and measurement packet losses. Under this constraint, we obtain a dynamic output feedback minimax controller. For the infinite-horizon case, we provide necessary and sufficient conditions in terms of the packet loss rates and the H^∞ disturbance attenuation parameter under which the minimax controller exists and is able to stabilize the closed-loop system in the mean-square sense. In particular, we show that unlike the corresponding LQG case, these conditions are coupled and therefore cannot be determined independently.

This paper considers a minimax control problem over multiple packet dropping channels. The channel losses are assumed to be Bernoulli processes, and operate under the transmission control protocol (TCP); hence acknowledgments of control and measurement drops are available at each time. Under this setting, we obtain an output feedback minimax controller, which are implicitly dependent on rates of control and measurement losses. For the infinite-horizon case, we first characterize achievable H^∞ disturbance attenuation levels, and then show that the underlying condition is a function of packet loss rates. We also address the converse part by showing that the condition of the minimum attainable loss rates for closed-loop system stability is a function of H^∞ disturbance attenuation parameter. Hence, those conditions are coupled with each other. Finally, we show the limiting behavior of the minimax controller under the disturbance attenuation parameter.