Networked LQG control over lossy channels with computational/packet-transmission delays and coarsely quantised packets

This article addresses the linear quadratic Gaussian (LQG) control problem of networked multi-input, multi-output systems where computational delay exists and the measurement and control signals are packetised and transmitted through a network within which random delay and packet loss may occur during transmissions. A transmission control protocol (TCP)-like protocol for the communication network is considered in which acknowledgement is sent from the actuator to the controller if and only if the control packet is received, assuming these acknowledgements always reach the estimator in time and without fail. To minimise the data word-length for transmissions over the network and to maximise control system performance, it is proposed that different quantisation resolutions be used for transmission data encapsulation, and control and output signals A/D-D/A conversions at sensor/actuator. To circumvent the problem of disparity between encapsulation and A/D-D/A quantisation resolutions, a pseudo-stochastic approach via subtractive dither is applied to quantise the transmission packets. This also enables us to model the quantisation errors as uncorrelated independent zero-mean additive white noises and apply standard LQG methodology and separation principle to design the estimator and the controller separately. An example is included to demonstrate the effectiveness of the approach.