Abstract-Sequential rate-distortion (SRD) theory provides a framework for studying the fundamental trade-off between datarate and data-quality in real-time communication systems. In this paper, we consider the SRD problem for multi-dimensional timevarying Gauss-Markov processes under mean-square distortion criteria. We first revisit the sensor-estimator separation principle, which asserts that considered SRD problem is equivalent to a joint sensor and estimator design problem in which data-rate of the sensor output is minimized while the estimator's performance satisfies the distortion criteria. We then show that the optimal joint design can be performed by semidefinite programming. A semidefinite representation of the corresponding SRD function is obtained. Implications of the obtained result in the context of zero-delay source coding theory and applications to networked control theory are also discussed.

The evolution of particle shape is an important consideration in many industrial crystallizations. This article describes the design of temperature-cycling experiments (between alternating positive and negative supersaturations) to substantially change crystal shape with only a small number of cycles. The growth and dissolution of monosodium glutamate crystals of varying shapes were monitored using in-process attenuated total reflection−Fourier transform infrared spectroscopy (ATR-FTIR), focused beam reflectance measurement (FBRM), particle vision and measurement (PVM), and off-line optical microscopy. The growth and dissolution kinetics were estimated in a multidimensional population balance model based on solute concentration and crystal dimension measurements. This model fitted the experimental data with a limited number of parameters of small uncertainty. In addition, with the estimated kinetic parameters, the model predicted the crystal size and shape distribution in a different temperature-cycling experiment reasonably well. In contrast to previous studies that have estimated kinetics along multiple crystal axes in mixed-tank crystallizers, this study implements dissolution terms in the multidimensional population balance model along multiple axes.

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