Maximization of Information in Energy Limited Directed Communication

This study is concerned with an observer who desires to inform optimally a distant agent regarding a physical stochastic process in the environment. We consider that the observer has a constraint on the energy resource for the directed communication to the agent. The information we are interested in is the change in the knowledge possessed by the agent about the state of the process. We find the maximum information that can be transferred from the observer to the agent over a finite horizon subject to a bound on the total energy of the observer.We show that the maximum information is the optimal value of a mixed-integer nonlinear optimization problem. We obtain lower and upper bounds on the maximum information and also a suboptimal admissible solution based on a semidefinite programming. Moreover, we propose an optimized event-triggering mechanism based on a linear matrix inequality which yields event-driven sampling. Numerical and simulation results are presented for simple stable and unstable systems.