On LQG joint optimal scheduling and control under communication constraints

In this paper, we consider a discrete-time stochastic system, where sensor measurements are sent over a network to the controller. The design objective is a non-classical multicriterion optimization problem for finite horizon, where the cost function consists of the linear quadratic cost reflecting the control performance and a communication cost penalizing information exchange between sensor and controller. It is shown that the joint optimization of scheduling and control can be separated into three subproblems: an optimal regulator problem, an estimation problem and an optimal scheduling problem. The obtained results are extended to TCP-like networks with random packet loss. In the proposed framework, we classify three classes of schedulers, a purely randomized, a deterministic and a state-dependent scheme, and compare their performance by a numerical example.