Optimal control over a packet-dropping network based on linear predictive compensation

This paper investigates the linear quadratic Gaussian (LQG) control problem over a packet-dropping network connecting the local sensor and the remote controller. A linear predictive compensator is proposed for counteracting the stochastic packet loss. The control command executes to the plant is first expressed as the random sequence which relies on the packet arrival sequence. The information set of the system is then divided into several subsets and corresponding prediction error covariances of each subset are also obtained. By this means, the quantitative relationship between the performance index of LQG control and the prediction steps is established. Numerical example shows that there exists finite steps of prediction for minimizing the performance index.