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Robust Causal Transform Coding for LQG Systems with Delay Loss in Communications

A networked controlled system (NCS) in which the plant communicates to the controller over a channel with random delay loss is considered. The channel model is motivated by recent development of tree codes for NCS, which effectively translates an erasure channel to one with random delay. A causal transform coding scheme is presented which exploits the plant state memory for efficient communications (compression) and provides robustness to channel delay loss. In this setting, we analyze the performance of linear quadratic Gaussian (LQG) closed-loop systems and the design of the optimal controller. The design of the transform code for LQG systems is posed as a channel optimized source coding problem of minimizing a weighted mean squared error over the channel. The solution is characterized in two steps of obtaining the optimized causal encoding and decoding transforms and rate allocation across a set of transform coding quantizers. Numerical and simulation results for Gauss-Markov sources and an LQG system demonstrate the effectiveness of the proposed schemes.