Continuous-time indefinite linear quadratic optimal control with random input gains

In this paper, the indefinite linear quadratic (LQ) optimal control of continuous-time linear time-invariant (LTI) systems with random input gains is studied. One main novelty of this work is the use of channel/controller co-design framework which bridges and integrates the design of the channels and controller. The co-design is carried out by the twist of channel resource allocation, i.e., the channel capacities can be allocated among the input channels by the control designer subject to an overall capacity constraint. With the channel/controller co-design, necessary and sufficient conditions for the well-posedness as well as the attainability of the indefinite LQ problem concerned are obtained. The optimal control law is given by a linear state feedback associated with the mean-square stabilizing solution of a modified algebraic Riccati equation.