Optimal control over multiple erasure channels using a data dropout compensation scheme

In this paper we focus on networked control systems subject to data dropouts. We consider that the controller communicates with the plant through multiple independent erasure channels, and that each actuator sends acknowledgement packages to the controller. We restrict our attention to the optimal design of a class of controllers that embeds a data dropout compensator and where, besides this compensation mechanism, all processing is an affine function of the available data. Our first result shows that the optimal design consists in solving, separately, an estimation problem and a control problem. The optimal controller is a linear function of the estimated state, which is obtained exploiting the information given by the acknowledgement packages and the data dropout compensator. Since we focus on a specific class of controllers, our proposal is suboptimal, however, unlike the optimal LQG controller found in the literature, our proposal is easier to implement, and its steady state behaviour can be simply determined. We also show that, under standard conditions, the affine part of the optimal controller converges to an LTI filter, which can be used as a simple alternative to the time varying controller.