A new compensation framework for LQ control over lossy networks

In this paper we study the compensation problem of LQ control over lossy networks under TCP-like protocols. The system we consider is discrete, linear, and time-invariant. Firstly, a general framework for static compensation is proposed. Secondly, using dynamic programming and optimization method we are able to get governing equations for the controller and the compensator gains that are optimized. Under the new framework, the two popular compensators: zero-input and hold-input appear to be special cases of the proposed one, and the issue as to why none of the above two commonly adopted compensation strategies can be claimed to be better than the other is to a great extent clarified. An iterative algorithm is also presented to solve the governing equations for the optimal gains obtained in the paper. Following that we provide two numerical examples to validate the new approach.