Finite Horizon LQ Optimal Control and Computation with Data Rate Constraints

This paper considers the optimal control of a linear scalar model with a finite communication rate between the sensor and the controller. We analyze the optimization of the quantizer and the controller where the latter utilizes the overall history of the received symbols to determine the control input. Making use of a tree structure representation, it is shown that the resulting optimal control problem can be reduced to a combined quantization and constrained quadratic minimization problem. We characterize the necessary conditions for the optimal control and develop numerical algorithms. A localized computational method for long time horizon is also discussed.