Control Under Action-Dependent Markov Packet Drops: An Event-Triggered Approach

Abstract: In this paper, we consider the problem of second moment stabilization of a scalar linear plant with process noise. We assume that the sensor must communicate with the controller over an unreliable channel, whose state evolves according to a Markov chain, with the transition matrix on a timestep depending on whether there is a transmission or not on that timestep. Under such a setting, we propose an event-triggered transmission policy which meets the objective of exponential convergence of the second moment of the plant state to an ultimate bound. Furthermore, we provide upper bounds on the transmission fraction of the proposed policy. The guarantees on performance and transmission fraction are verified using simulations.