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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 613 records · Page 34

Mapping Thermal Conductivity at the Atomic Scale: A Step toward the Thermal Design of Materials

We describe a spatial decomposition of the thermal conductivity, termed site-projected thermal conductivity, which quantifies the thermal conduction activity at each atomic site—a critical parameter for the thermal design of materials. The method is based on the Green–Kubo formula and the harmonic approximation and requires the force-constant and dynamical matrices, as well as a relaxed structural model. Throughout the study, it uses high quality models previously tested and compared to many experiments. It discusses the method and underlying approximations for amorphous silicon, carries the detailed analysis for amorphous silicon, and then examines an amorphous-crystal silicon interface and representative carbon materials. This study identifies the sites and local structures that reduce heat transport, and quantify these (estimate the spatial range) over which these “thermal defects” are effective. It identifies filamentary structures in the amorphous silicon network which impact heat transport and electronic structure (the Urbach edge) and electronic transport.

36 MATERIALS SCIENCE↗

A reduced-order model for nonlinear radiative transfer problems based on moment equations and POD-Petrov-Galerkin projection of the normalized Boltzmann transport equation

A data-driven projection-based reduced-order model (ROM) for nonlinear thermal radiative transfer (TRT) problems is presented. The TRT ROM is formulated by (i) a hierarchy of low-order quasidiffusion (aka variable Eddington factor) equations for moments of the radiation intensity and (ii) the normalized Boltzmann transport equation (BTE). The multilevel system of moment equations is derived by projection of the BTE onto a sequence of subspaces which represent elements of the phase space of the problem. Exact closure for the moment equations is provided by the Eddington tensor. A Petrov-Galerkin (PG) projection of the normalized BTE is formulated using a proper orthogonal decomposition (POD) basis representing the normalized radiation intensity over the whole phase space and time. The Eddington tensor linearly depends on the solution of the normalized BTE. By linear superposition of the POD basis functions, a low-rank expansion of the Eddington tensor is constructed with coefficients defined by the PG projected normalized BTE. The material energy balance (MEB) equation is coupled with the effective gray low-order equations which exist on the same dimensional scale as the MEB equation. The resulting TRT ROM is structure and asymptotic preserving. A detailed analysis of the ROM is performed on the classical Fleck-Cummings (F-C) TRT multigroup test problem in 2D geometry. Numerical results are presented to demonstrate the ROM's effectiveness in the simulation of radiation wave phenomena. Importantly, the ROM is shown to produce solutions with sufficiently high accuracy while using low-rank approximation of the normalized BTE solution. Essential physical characteristics of supersonic radiation wave are preserved in the ROM solutions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Interpretable and flexible non-intrusive reduced-order models using reproducing kernel Hilbert spaces

This paper develops an interpretable, non-intrusive reduced-order modeling technique using regularized kernel interpolation. Existing non-intrusive approaches approximate the dynamics of a reduced-order model (ROM) by solving a data-driven least-squares regression problem for low-dimensional matrix operators. Our approach instead leverages regularized kernel interpolation, which yields an optimal approximation of the ROM dynamics from a user-defined reproducing kernel Hilbert space. We show that our kernel-based approach can produce interpretable ROMs whose structure mirrors full-order model structure by embedding judiciously chosen feature maps into the kernel. The approach is flexible and allows a combination of informed structure through feature maps and closure terms via more general nonlinear terms in the kernel. We also derive a computable a posteriori error bound that combines standard error estimates for intrusive projection-based ROMs and kernel interpolants. In conclusion, the approach is demonstrated in several numerical experiments that include comparisons to operator inference using both proper orthogonal decomposition and quadratic manifold dimension reduction.

Data-driven model reduction↗

Extended dynamic mode decomposition for model reduction in fluid dynamics simulations

High computational cost and storage/memory requirements of fluid dynamics simulations constrain their usefulness as a predictive tool. Reduced-order models (ROMs) provide a viable solution to this challenge by extracting the key underlying dynamics of a complex system directly from data. We investigate the efficacy and robustness of an extended dynamic mode decomposition (xDMD) algorithm in constructing ROMs of three-dimensional cardiovascular computations. Focusing on the ROMs' accuracy in representation and interpolation, we relate these metrics to the truncation rank of singular value decomposition, which underpins xDMD and other approaches to ROM construction. Our key innovation is to relate the truncation rank to the singular values of the original flow problem. This result establishes a priori guidelines for the xDMD deployment and its likely success as a means of data compression and reconstruction of the system's dynamics from dominant spatiotemporal structures present in the data.

Mechanics↗

Asynchronous interactive control systems

A class of interactive control systems is derived by generalizing interactive manipulator control systems. The general structural properties of such systems are discussed and an appropriate general software implementation is proposed. This is based on the fact that tasks of interactive control systems can be represented as a network of a finite set of actions which have specific operational characteristics and specific resource requirements, and which are of limited duration. This has enabled the decomposition of the overall control algorithm into a set of subalgorithms, called subcontrollers, which can operate simultaneously and asynchronously. Coordinate transformations of sensor feedback data and actuator set-points have enabled the further simplification of the subcontrollers and have reduced their conflicting resource requirements. The modules of the decomposed control system are implemented as parallel processes with disjoint memory space communicating only by I/O. The synchronization mechanisms for dynamic resource allocation among subcontrollers and other synchronization mechanisms are also discussed in this paper. Such a software organization is suitable for the general form of multiprocessing using computer networks with distributed storage.

Vuskovic, M. I.↗

Computation of an Underexpanded 3-D Rectangular Jet by the CE/SE Method

Recently, an unstructured three-dimensional space-time conservation element and solution element (CE/SE) Euler solver was developed. Now it is also developed for parallel computation using METIS for domain decomposition and MPI (message passing interface). The method is employed here to numerically study the near-field of a typical 3-D rectangular under-expanded jet. For the computed case-a jet with Mach number Mj = 1.6. with a very modest grid of 1.7 million tetrahedrons, the flow features such as the shock-cell structures and the axis switching, are in good qualitative agreement with experimental results.

Loh, Ching Y.↗

Linkages between terrestrial ecosystems and the atmosphere

The primary research issue in understanding the role of terrestrial ecosystems in global change is analyzing the coupling between processes with vastly differing rates of change, from photosynthesis to community change. Representing this coupling in models is the central challenge to modeling the terrestrial biosphere as part of the earth system. Terrestrial ecosystems participate in climate and in the biogeochemical cycles on several temporal scales. Some of the carbon fixed by photosynthesis is incorporated into plant tissue and is delayed from returning to the atmosphere until it is oxidized by decomposition or fire. This slower (i.e., days to months) carbon loop through the terrestrial component of the carbon cycle, which is matched by cycles of nutrients required by plants and decomposers, affects the increasing trend in atmospheric CO2 concentration and imposes a seasonal cycle on that trend. Moreover, this cycle includes key controls over biogenic trace gas production. The structure of terrestrial ecosystems, which responds on even longer time scales (annual to century), is the integrated response to the biogeochemical and environmental constraints that develop over the intermediate time scale. The loop is closed back to the climate system since it is the structure of ecosystems, including species composition, that sets the terrestrial boundary condition in the climate system through modification of surface roughness, albedo, and, to a great extent, latent heat exchange. These separate temporal scales contain explicit feedback loops which may modify ecosystem dynamics and linkages between ecosystems and the atmosphere. The long-term change in climate, resulting from increased atmospheric concentrations of greenhouse gases (e.g., CO2, CH4, and nitrous oxide (N2O)) will further modify the global environment and potentially induce further ecosystem change. Modeling these interactions requires coupling successional models to biogeochemical models to physiological models that describe the exchange of water, energy, and biogenic trace gases between the vegetation and the atmosphere at fine time scales. There does not appear to be any obvious way to allow direct reciprocal coupling of atmospheric general circulation models (GCM's), which inherently run with fine time steps, to ecosystem or successional models, which have coarse temporal resolution, without the interposition of physiological canopy models. This is equally true for biogeochemical models of the exchange of carbon dioxide and trace gases. This coupling across time scales is nontrivial and sets the focus for the modeling strategy.

Bretherton, Francis↗

Source Decomposition of Eddy-Covariance CO 2 Flux Measurements for Evaluating a High-Resolution Urban CO 2 Emissions Inventory

We present the comparison of source-partitioned CO2 flux measurements with a high-resolution urban CO 2 emissions inventory (Hestia). Tower-based measurements of CO and 14 C are used to partition net CO 2 flux measurements into fossil and biogenic components. A flux footprint model is used to quantify spatial variation in flux measurements. We compare the daily cycle and spatial structure of Hestia and eddy-covariance derived fossil fuel CO 2 emissions on a seasonal basis. Hestia inventory emissions exceed the eddy-covariance measured emissions by 0.36 µ mol m −2 s −1 (3.2%) in the cold season and 0.62 µ mol m −2 s −1 (9.1%) in the warm season. The daily cycle of fluxes in both products matches closely, with correlations in the hourly mean fluxes of 0.86 (cold season) and 0.93 (warm season). The spatially averaged fluxes also agree in each season and a persistent spatial pattern in the differences during both seasons that may suggest a bias related to residential heating emissions. In addition, in the cold season, the magnitudes of average daytime biological uptake and nighttime respiration at this flux site are approximately 15% and 27% of the mean fossil fuel CO 2 emissions over the same time period, contradicting common assumptions of no significant biological CO 2 exchange in northern cities during winter. This work demonstrates the effectiveness of using trace gas ratios to adapt eddy-covariance flux measurements in urban environments for disaggregating anthropogenic CO 2 emissions and urban ecosystem fluxes at high spatial and temporal resolution.

eddy-covariance flux measurements↗

Root exudate lipids: Uncovering chemodiversity and carbon stability potential

Root-derived carbon has been shown to contribute more to soil carbon stocks than aboveground litter. Yet the molecular chemodiversity of root exudates remains poorly understood due to limited characterization and annotation. In this study, we characterized the molecular chemodiversity and production of metabolites and lipids in root exudates from field grown mature tall wheatgrass (Thinopyrum ponticum). We discovered a diversity of lipids, including substantial levels of triacylglycerols (∼19 μg/g fresh root per min), fatty acyls, sphingolipids, sterol lipids, and glycerophospholipids, some of which have not been previously documented in root exudates. By integrating tandem mass spectral library searching and deep learning-based chemical class assignment, our metabo-lipidomics approach significantly expanded the known molecular diversity of root exudates. Rates of lipid derived carbon production were approximately double that of polar metabolites (lipids: 81.52 ± 13.81 vs polar metabolites: 38.41 ± 5.93 μg C g −1 fresh root mass min −1 ) with an order of magnitude higher carbon to nitrogen ratios (lipids: 459 ± 90 vs polar metabolites: 14.40 ± 0.58). Exudate lipids displayed highly negative nominal oxidation state of carbon (−1.182 to −1.909), indicating that these compounds may be less favorable for microbial decomposition. Together our results suggest the potential of root exudate lipids to contribute to stable carbon pools in soil, supporting long-term carbon storage. This work advances understanding of plant-derived lipid inputs to soil and underscores the need for future studies on the functional roles of lipids in shaping root-microbe-soil interactions, microbial activity, soil structure, and nutrient availability – contributing to soil health.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Ecosystem Impacts of Woody Encroachment In Texas: A Spatial Analysis Using AVIRIS

Woody encroachment, the increase of woody plant density relative to herbaceous vegetation, has been documented in drylands of Texas as well as worldwide (Archer 1994, Harrington and Harman 1995, Moleele et al. 2002). Over-grazing, fire suppression and climate change are implicated in the shift from open grasslands to ecosystems now populated by trees and shrubs (Scholes and Archer 1997, Archer et al. 2001), such as Prosopis glandulosa var. glandulosa (honey mesquite) in north Texas (Teague et al. 1997, Ansley et al. 2001, Asner et al. 2003a). Several studies have examined changes in ecosystem properties accompanying woody vegetation encroachment in the Southwest U.S., with research focused on increases in plant and soil carbon (C) and nitrogen (N) stores (Hoffman and Jackson 2000, Asner et al. 2003a), isotopic shifts in these pools (Boutton 1999, Archer et al. 2001), and increases in N cycling rates (Rundel et al. 1982, Hibbard et al. 2001). However, little is known regarding the impact of woody encroachment on N trace gas emissions from dryland regions such as Texas. NOx is produced in the soil during the processes of nitrification and denitrification (Firestone and Davidson 1989). The total N efflux from soils is most directly influenced by the internal cycling of N, which at a regionalscale, is controlled by the inputs and availability of N from vegetation via litterfall and subsequent decomposition (Robertson et al. 1989). Although plot-scale studies are critical to understanding controls over N oxide emissions, regionalization of the measurements is impeded by spatial variation in the factors contributing most to N cycling processes: soil properties (affecting soil moisture regimes and N stocks) and vegetation cover (affecting litter inputs and N uptake). While broad patterns in ecosystem structure and vegetation composition co-vary with general patterns of trace gas emissions (Matson 1997), there is no easily measured index of N availability that can be applied for regional-scale studies of N oxide fluxes. Remote sensing is arguably the only approach available to develop a spatially-explicit understanding of ecosystem processes. More specifically, remotely detectable spatial patterns in the distal controls over soil N properties, such as vegetation cover, land use and soil type (Robertson et al. 1989), should be exploited for regional studies of N oxide emissions. The woody encroachment phenomenon provides an opportunity to test the strength of the relationship between N oxide emissions and those factors controlling the fluxes that can be remotely measured. If such linkages can be firmly established, and if the spatial pattern of distal controls is relevant, then the combination of field measurements and remote sensing offers to improve regional-scale N oxide estimates. The paper presents the utility of linking field based sampling of soil NOx emissions with very high resolution remote sensing estimates of woody vegetation cover from the NASA AVIRIS, Airborne Visible-Infrared Imaging Spectrometer (Green et al. 1998, Asner and Green 2001) and automated spectral mixture analysis (Asner and Lobell 2000, Asner and Heidebrecht 2002) that provide a means to spatially extrapolate soil NOx emissions to the regional scale.

Martin, Roberta E.↗

Using SpF to Achieve Petascale for Legacy Pseudospectral Applications

Pseudospectral (PS) methods possess a number of characteristics (e.g., efficiency, accuracy, natural boundary conditions) that are extremely desirable for dynamo models. Unfortunately, dynamo models based upon PS methods face a number of daunting challenges, which include exposing additional parallelism, leveraging hardware accelerators, exploiting hybrid parallelism, and improving the scalability of global memory transposes. Although these issues are a concern for most models, solutions for PS methods tend to require far more pervasive changes to underlying data and control structures. Further, improvements in performance in one model are difficult to transfer to other models, resulting in significant duplication of effort across the research community. We have developed an extensible software framework for pseudospectral methods called SpF that is intended to enable extreme scalability and optimal performance. Highlevel abstractions provided by SpF unburden applications of the responsibility of managing domain decomposition and load balance while reducing the changes in code required to adapt to new computing architectures. The key design concept in SpF is that each phase of the numerical calculation is partitioned into disjoint numerical kernels that can be performed entirely inprocessor. The granularity of domain decomposition provided by SpF is only constrained by the datalocality requirements of these kernels. SpF builds on top of optimized vendor libraries for common numerical operations such as transforms, matrix solvers, etc., but can also be configured to use open source alternatives for portability. SpF includes several alternative schemes for global data redistribution and is expected to serve as an ideal testbed for further research into optimal approaches for different network architectures. In this presentation, we will describe our experience in porting legacy pseudospectral models, MoSST and DYNAMO, to use SpF as well as present preliminary performance results provided by the improved scalability.

DYNAMO↗

Second Generation RLV Space Vehicle Concept

NASA has a long history of conducting development programs and projects in a consistent fashion. Systems Engineering within those programs and projects has also followed a given method outlined by such documents as the NASA Systems Engineering Handbook. The relatively new NASA Space Launch Initiative (SLI) is taking a new approach to developing a space vehicle, with innovative management methods as well as new Systems Engineering processes. With the program less than a year into its life cycle, the efficacy of these new processes has yet to be proven or disproven. At $776M for phase 1, SLI represents a major portion of the NASA focus; however, the new processes being incorporated are not reflected in the training provided by NASA to its engineers. The NASA Academy of Program and Project Leadership (APPL) offers core classes in program and project management and systems engineering to NASA employees with the purpose of creating a "knowledge community where ideas, skills, and experiences are exchanged to increase each other's capacity for strong leadership". The SLI program is, in one sense, a combination of a conceptual design program and a technology program. The program as a whole doesn't map into the generic systems engineering project cycle as currently, and for some time, taught. For example, the NASA APPL Systems Engineering training course teaches that the "first step in developing an architecture is to define the external boundaries of the system", which will require definition of the interfaces with other systems and the next step will be to "define all the components that make up the next lower level of the system hierarchy" where fundamental requirements are allocated to each component. Whereas, the SLI technology risk reduction approach develops architecture subsystem technologies prior to developing architectures. The higher level architecture requirements are not allowed to fully develop and undergo decomposition and allocation down to the subsystems before the subsystems must develop allocated requirements based on the highest level of requirements. In the vernacular of the project cycles prior to the mid 1990's, the architecture definition portion of the program appears to be at a generic Phase A stage, while the subsystems are operating at Phase B. Even the management structure of the SLI program is innovative in its approach to Systems Engineering and is not reflected in the APPL training modules. The SLI program has established a Systems Engineering office as an office separate from the architecture development or the subsystem technology development, while that office does have representatives within these other offices. The distributed resources of the Systems Engineering Office are co-located with the respective Project Offices. This template is intended to provide systems engineering as an integrated function at the Program Level. the program management of SLI and the MAT agree that "program/project managers and the systems engineering team must work closely together towards the single objective of delivering quality products that meet the customer needs". This paper will explore the differences between the methods being taught by NASA, which represent decades of ideas, and those currently in practice in SLI. Time will tell if the innovation employed by SLI will prove to be the model of the future. For now, it is suggested that the training of the present exercise the flexibility of recognizing the new processes employed by a major new NASA program.

Bailey, Michelle↗

SpF: Enabling Petascale Performance for Pseudospectral Dynamo Models

Pseudospectral (PS) methods possess a number of characteristics (e.g., efficiency, accuracy, natural boundary conditions) that are extremely desirable for dynamo models. Unfortunately, dynamo models based upon PS methods face a number of daunting challenges, which include exposing additional parallelism, leveraging hardware accelerators, exploiting hybrid parallelism, and improving the scalability of global memory transposes. Although these issues are a concern for most models, solutions for PS methods tend to require far more pervasive changes to underlying data and control structures. Further, improvements in performance in one model are difficult to transfer to other models, resulting in significant duplication of effort across the research community.We have developed an extensible software framework for pseudospectral methods called SpF that is intended to enable extreme scalability and optimal performance. High-level abstractions provided by SpF unburden applications of the responsibility of managing domain decomposition and load balance while reducing the changes in code required to adapt to new computing architectures. The key design concept in SpF is that each phase of the numerical calculation is partitioned into disjoint numerical kernels that can be performed entirely in-processor. The granularity of domain-decomposition provided by SpF is only constrained by the data-locality requirements of these kernels. SpF builds on top of optimized vendor libraries for common numerical operations such as transforms, matrix solvers, etc., but can also be configured to use open source alternatives for portability. SpF includes several alternative schemes for global data redistribution and is expected to serve as an ideal testbed for further research into optimal approaches for different network architectures.In this presentation, we will describe the basic architecture of SpF as well as preliminary performance data and experience with adapting legacy dynamo codes. We will conclude with a discussion of planned extensions to SpF that will provide pseudospectral applications with additional flexibility with regard to time integration, linear solvers, and discretization in the radial direction.

Pseudospectral (PS)↗

Numerical Investigation and Optimization of a Flushwall Injector for Scramjet Applications at Hypervelocity Flow Conditions

An investigation utilizing Reynolds-averaged simulations (RAS) was performed in order to demonstrate the use of design and analysis of computer experiments (DACE) methods in Sandia’s DAKOTA software package for surrogate modeling and optimization. These methods were applied to a flow- path fueled with an interdigitated flushwall injector suitable for scramjet applications at hyper- velocity conditions and ascending along a constant dynamic pressure flight trajectory. The flight Mach number, duct height, spanwise width, and injection angle were the design variables selected to maximize two objective functions: the thrust potential and combustion efficiency. Because the RAS of this case are computationally expensive, surrogate models are used for optimization. To build a surrogate model a RAS database is created. The sequence of the design variables comprising the database were generated using a Latin hypercube sampling (LHS) method. A methodology was also developed to automatically build geometries and generate structured grids for each design point. The ensuing RAS analysis generated the simulation database from which the two objective functions were computed using a one-dimensionalization (1D) of the three-dimensional simulation data. The data were fitted using four surrogate models: an artificial neural network (ANN), a cubic polynomial, a quadratic polynomial, and a Kriging model. Variance-based decomposition showed that both objective functions were primarily driven by changes in the duct height. Multiobjective design optimization was performed for all four surrogate models via a genetic algorithm method. Optimal solutions were obtained at the upper and lower bounds of the flight Mach number range. The Kriging model predicted an optimal solution set that exhibited high values for both objective functions. Additionally, three challenge points were selected to assess the designs on the Pareto fronts. Further sampling among the designs of the Pareto fronts may be required to lower the surrogate model errors and perform more accurate surrogate-model-based optimization.

Shenoy, Rajiv R.↗

Autonomous direct freeform fabrication strategy for multi-axis additive manufacturing

Multi-axis additive manufacturing (M-AM) enables precise material deposition along both planar and curved layers, eliminating the need for support structures through a continuous material deposition approach. In contrast to conventional 2-dimensional planar layers constrained to a fixed building orientation, the deposition on freeform layers demands the specification of guided curves to determine material deposition directions which are no longer to be fixed to a build direction. There are challenges that arise when fabricating components with multiple “build” directions, necessitating the decomposition of geometries and the specification of guided curves for the resulting volumes. Furthermore, multi-axis systems introduce heightened challenges due to an increased degree of freedom in motion. Consequently, the potential risks of collision between the deposited geometry and the motion platform become a notable concern. This research proposes a freeform layering algorithm to address the challenge of seamless transitions between planar and curved layers in the process planning of M-AM. The algorithm computes 3D “printable” layers by leveraging topological information derived from the geometry to be built and integrates collision-free manufacturability considerations into the computational process. These accumulated volumes serve as a “substrate” and support volumes for subsequent deposition, allowing later layers to be built without the need for additional support material. In conclusion, the proposed method successfully devises a freeform layering approach suitable for intricate models that demand substantial support, thus enabling the fabrication of diverse geometries in a manner previously unachievable.

36 MATERIALS SCIENCE↗

An unusual Co–S bond links B 12 chaperones in an interprotein complex

Chaperones in trafficking pathways ensure specificity of transition metal loading and protection against adventitious side reactions. In B 12 , an essential cofactor for humans, a cobalt ion is coordinated to a >1.3 kDa tetrapyrrolic scaffold, posing logistical challenges for its translocation. In this study, we report the 3.4 Å crystal structure of the human MMACHC and MMADHC B 12 chaperones, tethered via a rarely seen covalent cobalt–sulfur bond. B 12 is bound in the base-off state to MMACHC, with Cys-261 on MMADHC serving as the upper axial ligand; the lower-axial position is vacant. The propensity of thiolato-cobalamin derivatives bound to MMACHC to undergo spontaneous decomposition via general acid catalysis or reduction/oxidation chemistry is averted in the interprotein complex with MMADHC. An exposed face in the complex suggests an exit route for B 12 . No known clinical variants localize to the interprotein interface, consistent with the cobalt–sulfur bond being key to forming the high-affinity complex.

Science & Technology - Other Topics↗

Decentralization, stabilization, and estimation of large-scale linear systems

In this short paper we consider three closely related aspects of large-scale systems: decentralization, stabilization, and estimation. A method is proposed to decompose a large linear system into a number of interconnected subsystems with decentralized (scalar) inputs or outputs. The procedure is preliminary to the hierarchic stabilization and estimation of linear systems and is performed on the subsystem level. A multilevel control scheme based upon the decomposition-aggregation method is developed for stabilization of input-decentralized linear systems Local linear feedback controllers are used to stabilize each decoupled subsystem, while global linear feedback controllers are utilized to minimize the coupling effect among the subsystems. Systems stabilized by the method have a tolerance to a wide class of nonlinearities in subsystem coupling and high reliability with respect to structural perturbations. The proposed output-decentralization and stabilization schemes can be used directly to construct asymptotic state estimators for large linear systems on the subsystem level. The problem of dimensionality is resolved by constructing a number of low-order estimators, thus avoiding a design of a single estimator for the overall system.

Siljak, D. D.↗