We consider a discrete-time linear quadratic Gaussian networked control setting where the (full information) observer and controller are separated by a fixed-rate noiseless channel. The minimal rate required to stabilize such a system has been well studied. However, for a given fixed rate, how to quantize the states so as to optimizeperformance is an open question of great theoretical and practical significance. We concentrate on minimizing the control cost for first-order scalar systems. To that end, we use the Lloyd-Max algorithm and leverage properties of logarithmically-concave functions and sequential Bayesian filtering to construct the optimal quantizer that greedily minimizes the cost at every time instant. By connecting the globally optimal scheme to the problem of scalar successive refinement, we argue that its gain over the proposed greedy algorithm is negligible. This is significant since the globally optimal scheme is often computationally intractable. All the results are proven for the more general case of disturbances with logarithmically-concave distributions and rate-limited time-varying noiseless channels. We further extend the framework to event-triggered control by allowing to convey information via an additional "silent symbol", i.e., by avoiding transmitting bits; by constraining the minimal probability of silence we attain a tradeoff between the transmission rate and the control cost for rates below one bit per sample.

Articles you may be interested inRelatively low temperature synthesis of hexagonal tungsten carbide films by N doping and its effect on the preferred orientation, phase transition, and mechanical properties NbN films are deposited using direct current reactive magnetron sputtering in discharge of a mixture of N 2 and Ar gas, and the effects of substrate bias ͑V b ͒ on the preferred orientation, phase transition, and mechanical properties for NbN films are explored by x-ray diffraction, selective area electron diffraction, and nanoindentation measurements. It is found that V b has a significant influence on the stress in NbN films, leading to a pronounced change in the preferred orientation, phase structure, and hardness. As the substrate is at voltage floating, the stress is tensile. In contrast, as negative V b is applied, the stress becomes compressive, and increases with increasing the absolute value of negative V b . It is observed that a phase transition from ␦ ͑face-centered cubic͒ to ␦Ј ͑hexagonal͒ for NbN films occurs as V b is in the range of −80 to − 120 V, which can be attributed to a decrease in the strain energy for NbN films. In order to explore the relationship between the stress and phase transition as well as preferred orientation, density-functional theory based on first principles is used to calculate the elastic constants and shear modulus for NbN with a structure of ␦ or ␦Ј. The calculated results show that the shear modulus for ␦Ј-NbN is larger than that for ␦-NbN, whereas the bulk modulus for ␦Ј-NbN is almost equal to that for ␦-NbN, resulting in a difference in hardness for ␦or ␦Ј-NbN single crystal.

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We deposit niobium nitride (NbN) thin films on Si(1 0 0) substrates using direct current (dc) reactive magnetron sputtering in discharging a mixture of N2 and Ar gas, and explore the effects of nitrogen flow rate ( ) on the preferred orientation (PO), phase transition and mechanical properties for the obtained films by virtue of x-ray diffraction and nanoindentation measurements. We find that with increasing the biaxial compressive stress increases, which leads to a pronounced change in the PO and phase structure for the film. A phase transition from δ (face-centred cubic) to δ′ (hexagonal) occurs in the film as the biaxial stress increases to a critical value of about 3.9 GPa, which can be attributed to a decrease in the strain energy. With a further increase in the biaxial stress, the fraction of the δ′ phase in the film increases, and finally the film only has a single phase, δ′-NbN, resulting in a consistent increase in hardness.

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