Decentralized observers with consensus filters for distributed discrete-time linear systems

This paper presents a decentralized observer with a consensus filter for the state observation of discrete-time linear distributed systems. Each agent in the distributed system has an observer with a model of the plant that utilizes the set of locally available measurements, which may not make the full plant state detectable. This lack of detectability is overcome by utilizing a consensus filter that blends the state estimate of each agent with its neighbors’ estimates. It is proven that the state estimates of the proposed observer exponentially converge to the actual plant states under arbitrarily changing, but connected, communication and pseudo-connected sensing graph topologies. Except these connectivity properties, full knowledge of the sensing and communication graphs is not needed at the design time. As a byproduct, we obtained a result on the location of eigenvalues, i.e., the spectrum, of the Laplacian for a family of graphs with self-loops.     

Effects of Particle Size on the Fusion of Soda–Lime–Silicate Glass Containing NaCl

The coupled effects of particle size and 1 wt% NaCl additions on the sequence of melting reactions in a multicomponent system (sand–soda ash–calcite–dolomite–feldspar) were studied using data from DTA, DTGA, and XRD interactively. Glass batches varied in average particle size from 250 μm to finer than 45 μm. Milestone events in the fusion process of the coarse particle base glass were elucidated. The termination temperature of the last significant reaction associated with CO₂ release was 35°C lower in the fine particle size batch than with the coarsest batch. Liquid-phase formation at ∼523°C in the batch with 1 wt% NaCl occurred to an increasingly sizable extent with decreasing particle size. This contrasts with a similar effect at ∼630°C for a comparable batch without NaCl via eutectic melting between soda ash and dolomite. Sodium chloride additions significantly enhanced dissolution of CaO relic.     

Infrared reflectance and transmission spectra of semiconducting non-stoichiometric CdGe x As2

The infrared reflectance and transmission spectra of amorphous CdGe _x As₂ were investigated to study the amorphous structure with varying Ge content. The mid-infrared optical absorption edges of amorphous CdGe _x As₂ with 0<x<1.2, were observed in the range 1.6–1.7 m, indicating a structural similarity in short-range order throughout. Comparing the reflectance and transmission spectra of amorphous and devitrified crystalline phases established that the structures of amorphous CdGe _x As₂ transformed from the CdAs₂ basic structure to the chalcopyrite (CdGeAs₂) structure, as one progressed fromx=0 tox=1.2. The infrared spectra were interpreted interactively with radial distribution function, magnetic susceptibility, density measurements, and crystallization studies. The crystallization behaviour of amorphous CdGe _x As₂ that was heat treated at different temperatures was investigated using far-infrared transmission spectra.     

Effect of matrix liquid phase on interphase formation in SiC fibre-reinforced Si2N2O-Al2O3-CaO composites

Matrix compositions based on Si₂N₂O, with Al₂O₃ and CaO additions, were used to hot press Nicalon SiC fibre-reinforced composites at 1600 °C. With both CaO and Al₂O₃ additions, eutectic melting formed an appreciable volume of liquid phase during hot pressing, which remained as a stable glassy phase in the cooled composites. This liquid phase fostered formation of 240 nm thick carbon-rich interphases between the fibres and the matrix. These interphases showed relatively low interfacial shear strength and resulted in composites which showed non-catastrophic, notch-independent fracture. Matrices using either Al₂O₃ or CaO did not form adequate liquid phase to form coarse interphases, and fracture was catastrophic in nature. Post-heat treatment of the composites at 1000 °C showed peripheral oxidation (removal of the carbon content of the interphase) indicating limited protection afforded when glassy phase was present in the matrix. Controlled cooling in the hot press did not cause the liquid regions to devitrify.     

A game theoretic fault detection filter

The fault detection process is approximated with a disturbance attenuation problem. The solution to this problem, for both linear time-varying and time-invariant systems, leads to a game theoretic filter which bounds the transmission of all exogenous signals except the fault to be detected. In the limit, when the disturbance attenuation bound is brought to zero, a complete transmission block is achieved by embedding the nuisance inputs into an unobservable, invariant subspace. Since this is the same invariant subspace structure seen in some types of detection filters, we can claim that the asymptotic game filter is itself a detection filter. One can also make use of this subspace structure to reduce the order of the limiting game theoretic filter by factoring this invariant subspace out of the state space. The resulting lower dimensional filter will then be sensitive only to the failure to be detected. A pair of examples given at the end of the paper demonstrate the effectiveness of the filter for time-invariant and time-varying problems in both full-order and reduced-order forms     

A stochastic controller for a scalar linear system with additive Cauchy noise

A stochastic control scheme is developed for scalar, discrete-time, and linear-dynamic systems driven by Cauchy distributed process and measurement noises. When addressing the optimal control problem for such systems, the standard quadratic cost criteria cannot be used. In this study we introduce a new objective function that is functionally similar to the Cauchy probability density function. The performance index, defined as the expectation of this objective function with respect to the Cauchy densities, exists. The dynamic programming solution to the fixed and finite horizon optimal control problem that uses this performance index appears to be intractable. Therefore, a moving horizon optimal model predictive control problem is implemented, for which the conditional expected value of the objective function and its gradients can be computed in closed   form and without assumptions such as certainty equivalence. Numerical results are shown for this m$m$-step model predictive optimal controller and compared to a similar, Linear-Exponential-Gaussian model predictive controller. An essential difference between the Cauchy and Gaussian controllers when applied to a system with Cauchy noises is that, while the Gaussian controller is linear and reacts strongly to all noise pulses, the Cauchy controller can differentiate between measurement and process noise pulses by ignoring the former while responding to the latter. This property of the Cauchy controller occurs when an impulsive measurement noise is more likely than an impulsive process noise. The Cauchy and Gaussian controllers react similarly when applied to a system with Gaussian noises, demonstrating the robustness of the proposed control scheme.     

The periodic optimality of LQ controllers satisfying strong stabilization

An LQ strong stabilization problem is proposed. To determine when a controller with periodic gains is locally superior to a linear time invariant compensator for this problem, a Π test is presented. For systems with strictly proper transfer functions, it is proven that the frequency range where stable periodic controllers based on weak variations about the LTI case can give better performance than stable LTI compensators is finite. In the development, a means to evaluate the second partials of functions with respect to matrix-valued parameters is introduced. For those systems where periodic control is warranted, techniques for designing optimal periodic strongly stabilizing controllers are presented. Two examples detailing the application of the Π test are provided, as well as an optimal periodic controller design example.     

Crystallization of Li2O · Al2O3· 6SiO2 Glasses Containing Niobium Pentoxide as Nucleating Dopant

Niobium pentoxide (T form, orthorhombic system) was utilized to promote devitrification in Li₂O · Al₂O₃· 6SiO₂ glasses. Two or more mole percentage of this nucleating dopant enhanced crystallization in these glasses. Glasses containing 4.0 and 8.0 mol% T-Nb₂O₅ exhibited a high tendency to form dispersed TT-Nb₂O₅ (monoclinic system) precipitates during the glass quenching process. The crystallization process in glasses containing 2.0 or 4.0 mol% T-Nb₂O₅ occurred as microphase separation, followed by the formation of dispersed TT-Nb₂O₅ crystalline precipitates (760°C), followed by β-quartz solid-solution ( ss ) formation (850° to 900°C) heterogeneously nucleated from the precipitates. β-quartz( ss ) transformed to β-spodumene( ss ), along with a polymorphic transition from the TT-Nb₂O₅ to M-Nb₂O₅ (tetragonal system) crystalline phase.     

Stability of Molybdenum Disilicide in Combustion Gak Environments

The stability of MoSi₂ in combustion gas at 1370° and 1600°C was evaluated using SOLGASMIX-PV thermodynamic modeling, periodic weight measurements, and characterization via XRD, SEM, EDS, and image analysis. Passive oxidation occurred at both temperatures. During an initial stage of exposure, specimen surfaces oxidized to form MoO_3(g) and amorphous SiO₂ via reduction of CO₂ and H₂O. After a short time (<6.5 min at 1370°C, <1 min at 1600°C), the oxidation mechanism switched; Mo₅Si₃ and amorphous SiO₂ formed as oxidation products. The first mechanism esulted in the formation of 46.1 vol% at 1370°C and 42.6 vol% at 1600°C of the amorphous silica surface coating. The attainment of a near-terminal weight gain implied silica formation was limited by H₂O and CO₂ diffusion through the silica coating.