Minimal Feedback Optimal Control of Linear-Quadratic-Gaussian Systems: No Communication is also a Communication

摘要

We consider a linear-quadratic-Gaussian optimal control problem where the sensor and the controller are remotely connected over a communication channel. The communication of the measurement from the sensor to the controller requires a certain cost which is augmented with the quadratic control cost. We formulate a control and communication co-design problem where we solve for the joint optimal pair of controller and transmitter. We emphasize on the fact that absence of measurement communication at any time instance also conveys certain information to the controller, and such implicit information should be taken into account while designing a controller. We decompose the problem into two subproblems to construct the optimal controller and the optimal transmitter. While the optimal controller can be constructed by solving a certain Riccati equation, the optimal transmitter can be found solving a certain dynamic programming problem. We first characterize a sub-optimal solution for this dynamic program and then design an iterative algorithm to further improve the sub-optimal solution.