A channel/controller co-design approach for infinite-horizon LQR problem with random input gains

This paper investigates the infinite-horizon linear quadratic regulator (LQR) problem of continuous-time LTI systems with random gains imposed on the input channels. The main novelty of this work originates from the point of view that in networked control, designing the channels and controller jointly often leads to an easier problem and meanwhile achieves better performance than designing them separately. Specifically, we formulate the LQR problem with random input gains as a channel/controller co-design problem. Such co-design can be realized by the twist of channel resource allocation, i.e., the channel capacities can be allocated among the input channels subject to an overall capacity constraint. The LQR problem is shown to be attainable under such co-design if and only if a modified algebraic Riccati equation (MARE) has a mean-square (MS) stabilizing solution. The optimal controller is given by a linear state feedback associated with the MS stabilizing solution. Moreover, a Newton's type iteration is developed for the computation of the MS stabilizing solution to the MARE.