Minimal Feedback Optimal Control of Linear-Quadratic-Gaussian Systems: No Communication is also a Communication
Conference : 21st International Federation of Automatic Control (IFAC) pp. 2231-2237 , Berlin
Date: July 12 - July 17, 2020
Abstract: 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 sensor to controller requires a certain cost which is augmented with the quadratic control performance cost. We formulate the control and communication co-design problem where we seek for the joint optimal controller and transmitter. We emphasize on the fact that absence of communication at any time instance also conveys certain information, and such implicit information should be taken into account. 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 dynamic programming problem for which we provide an algorithm.
Keywords: LQG systems, Optimal Control, Control Communication co-design,