Stochastic event-based LQG control: An analysis on strict consistency

This paper studies the discrete-time linear–quadratic-Gaussian problem under partial-information-based sensors and event-based transmissions. By constructing a special form of stochastic event-based protocols, the optimal control policy is obtained, which minimizes an average quadratic cost function under a fixed transmission protocol. Then, analytical expressions of the corresponding transmission and control performance are derived. To evaluate the efficiency of event-based protocols, the concept of strict consistency is introduced, which requires that the control performance of event-based protocols be strictly better than that of the periodic protocol under the same transmission rate. Based on the obtained analytical expressions, the strict consistency is proved by showing that the periodic protocol corresponds to a local maximum point in the design space of parameters. To further improve the control performance of stochastic event-based protocols, an iterative parameter design algorithm (with finite iterations) is proposed for ensuring a strict reduction in cost functions after each iteration. Finally, numerical simulations are provided to illustrate the theoretical results.