A stochastic approach to optimal switching between control and observation

This paper solves a control problem for a stochastic system, under the basic constraint that the feedback control signal and the observations from the system cannot use the communication channel simultaneously. Hence, two modes of operation result: 1) an observation mode where outputs from the system are transmitted to the controller, and no inputs are sent back to the plant, 2) a control mode where the output of the plant is decoupled from the controller, but control signals are transmitted back to the plant. We look for an optimal periodic regime in a statistical steady state by switching between the observation and the control mode. For this, the optimal gains for the control and the observer in either mode and the duty cycle are determined. This is solved by considering the deterministic model for the second order information state (the covariances). In addition, we show that the observation mode can be reduced to a lower order model, which leads to a multi-mode multi-dimensional problem