Robust control of LTI systems over unreliable communication channels with unreliable acknowledgments

We consider the robust (H
^∞
) control problem for linear time-invariant systems over unreliable communication channels that are subject to packet losses from sensors to the controller and from the controller to the actuators. Moreover, the acknowledgments of control packet transmissions are also sent over reverse unreliable communication channels, which is known as the quasi-TCP model. The robust control problem is formulated within a stochastic zero-sum dynamic game framework, from which we obtain an H
^∞
controller that minimizes the worst-case cost function in the presence of an adversary in the dynamical system. We characterize a set of existence conditions of the H
^∞
controller in terms of the disturbance attenuation parameter γ and packet loss rates. For the least disturbance attenuation scenario (as γ → 8), we show that the H
^∞
control system converges to the corresponding LQG system. We also show that the H
^∞
controller for the TCP- and UDP-cases can be arrived at as appropriate limits of the solution for the quasi-TCP problem. Numerical examples are presented to illustrate the theoretical results.