An Optimal Compensation Framework for Linear Quadratic Gaussian Control Over Lossy Networks

In this technical note, we study the compensation problem of LQG control over two lossy networks under TCP-like protocols and propose a new static and latest-control based compensation framework. Compared to two popular strategies, the zero-input and hold-input compensators and the recent generalized hold-input compensator by Moayedi et al. our new one is more general. The contribution of the new framework is in three aspects. Firstly, it takes the problem of LQG control over lossy networks to a new level by suggesting that the original problem should be more properly posed as a two-variable instead of a one-variable optimization problem. Secondly, it links the compensator gain selection and the minimization of quadratic cost together and bridges the gap between the two by providing an optimal gain selection. Thirdly, it incorporates the above three classes of compensators as special cases. The issue as to why none of the zero-input and hold-input compensation strategies can be claimed to be better than the other is to a great extent settled. Performance comparisons of the proposed method and the predictive outage compensator by Henriksson et al. and the generalized hold-input strategy by Moayedi et al. are made through numerical examples.