Optimal control over a lossy communication network based on linear predictive compensation

This study investigates the linear quadratic Gaussian state regulation problem over a packet-dropping network. A linear predictive compensation scheme is proposed to counteract the uncontrollable packet loss. To characterise the operating state of the system, differently from the widely used Markov jump linear systems theory or multi-mode Markov chain, in this study the actual control command executed to the plant is expressed as a stochastic sequence. Moreover, the original information set is divided into several subsets, which benefits to establish the quantitative relationship between the infinite-horizon quadratic performance index and the prediction horizon. A numerical example is provided to show that there exists an optimal prediction horizon to minimise the performance index.