Search NASA⌕ Search

SEARCH · Search NASA

Results for “Integrally Formed”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 685 records · Page 38
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Conceptual Basis and Techno-Economic Modeling for Integrated Algal Biorefinery Conversion of Microalgae to Fuels and Products (2019 NREL TEA Update: Highlighting Paths to Future Cost Goals via a New Pathway for Combined Algal Processing)

The report documents the conceptual basis for a new potential Combined Algal Processing design strategy which may allow more flexibility in accommodating different algal biomass feedstock compositions, by enabling upgrading of both protein and carbohydrates in a single step, without a strict requirement for either component to be in soluble or monomeric form, while maintaining effective wet lipid extraction techniques to enable high lipid recoveries. In light of previously-established constraints around algal biomass costs (which are significantly higher than lignocellulosic terrestrial biomass), the present CAP processing strategy reflects an integrated biorefinery concept producing both fuels and value-added chemical coproducts as a means to improve profitability and generate coproduct revenues to help drive down the minimum fuel selling price (MFSP) towards economically viable levels. Namely, this report highlights an integrated CAP biorefinery process and associated technical targets that would be required to achieve U.S. Department of Energy target MFSP goals of $2.5/gallon gasoline equivalent by 2030. This is accomplished by a process involving low-cost seasonal storage of algal biomass during high-growth seasons, rapid flash hydrolysis pretreatment of the biomass, solvent extraction of pretreated biomass, cleanup and fractionation of lipids into triglyceride and free fatty acid fractions, and a series of thermochemical conversion steps to upgrade carbohydrates and protein to hydrocarbon fuels. These steps include mild oxidative treatment (MOT), a process originally investigated at NREL for upgrading lignin, followed by catalytic ketonization and hydrotreating of MOT products to fuels. Isolated triglycerides are sent to a coproduct train, with the base case focused on upgrading to polyurethane foams as a high-value, high-market-volume coproduct.

09 BIOMASS FUELS↗
DOE OSTI2023

Photoexcitation of Fe 3 O Nodes in MOF Drives Water Oxidation at pH=1 When Ru Catalyst Is Present

Abstract Artificial photosynthesis strives to convert the energy of sunlight into sustainable, eco‐friendly solar fuels. However, systems with light‐driven water oxidation reaction (WOR) at pH=1 are rare. Broadly used [Ru(bpy) 3 ] 2+ (bpy=2,2’‐bipyridine) photosensitizer has a fixed +1.23 V potential which is insufficient to drive most water oxidation catalysts (WOCs) in acid, while Fe 2 O 3 , featuring the highly oxidizing holes, is not stable at low pH. Here, the key examples of Fe‐based metal–organic framework (MOF) water oxidation photoelectrocatalysts active at pH=1 are presented. Fe‐MIL‐126 and Fe MOF‐dcbpy structures were formed with 4,4’‐biphenyl dicarboxylate (bpdc), 2,2’‐bipyridine‐5,5’‐dicarboxylate (dcbpy) linkers and their mixtures. Presence of dcbpy linkers allows integration of metal‐based catalysts via coordination to 2,2’‐bipyridine fragments. Fe‐based MOFs were doped with Ru‐based precursors to achieve highly active MOFs bearing [Ru(bpy)(dcbpy)(H 2 O) 2 ] 2+ WOC. Materials were analyzed with X‐ray diffraction (XRD), scanning electron microscopy (SEM), Fourier transform infra‐red (FTIR) spectroscopy, resonance Raman, X‐ray absorption spectroscopy, fs optical pump‐probe, electron paramagnetic resonance (EPR), diffuse reflectance and electric conductivity measurements and were modeled by band structure calculations. It is shown that under reaction conditions, Fe III and Ru III oxidation states are present, indicating rate‐limiting electron transfer in MOF. Fe 3 O nodes emerge as photosensitizers able to drive prolonged O 2 evolution in acid. Further developments are possible via MOF's linker modification for enhanced light absorption, electrical conductivity, reduced MOF solubility in acid, Ru‐WOC modification for faster WOC catalysis, or Ru‐WOC substitution to 3d metal‐based systems. The findings give further insight for development of light‐driven water splitting systems based on Earth‐abundant metals.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Joining of High Strength Low Ductility AA7055 by Friction Self-piercing Rivet

High strength aluminum (Al) alloy is one of higher specific strength materials for decarbonization in transportation industries. Because of low ductility at room temperature, conventional mechanical fastening such as self-piercing riveting produces cracks at the joint. In this work, we applied friction self-piercing riveting to join Al alloy (AA) 7055. No cracks were observed in the joints because of the improved local ductility of Al alloy by the generated frictional heat during joining step. Numerical modeling of joining process was applied to guide rivet geometry design and rivet material strength. Mechanical integrity of the AA7055 joints was assessed by lap shear tensile and cross-tension testing. Metallurgical characterizations revealed solid-state bonding formed not only between the rivet and surround Al materials, but also upper and lower Al sheets at the joint interface. Both solid-state bonding and mechanical interlocking between the flared rivet and bottom AA7055 sheet were the major joint mechanisms.

Lim, Yong Chae↗
DOE OSTI2023

Measurement of the cross section of $$ {e}^{+}{e}^{-}\to {\Xi}^{-}{\overline{\Xi}}^{+} $$ at center-of-mass energies between 3.510 and 4.843 GeV

Abstract Usinge + e − collision data corresponding to a total integrated luminosity of 12.9 fb −1 collected with the BESIII detector at the BEPCII collider, the exclusive Born cross sections and the effective form factors of the reaction$$ {e}^{+}{e}^{-}\to {\Xi}^{-}{\overline{\Xi}}^{+} $$ e + e − → Ξ − Ξ ¯ + are measured via the single baryon-tag method at 23 center-of-mass energies between 3.510 and 4.843 GeV. Evidence for the decay$$ \psi (3770)\to {\Xi}^{-}{\overline{\Xi}}^{+} $$ ψ 3770 → Ξ − Ξ ¯ + is observed with a significance of 4.5σby analyzing the measured cross sections together with earlier BESIII results. For the other charmonium(-like) statesψ(4040),ψ(4160),Y(4230),Y(4360),ψ(4415), andY(4660), no significant signal of their decay to$$ {\Xi}^{-}{\overline{\Xi}}^{+} $$ Ξ − Ξ ¯ + is found. For these states, upper limits of the products of the branching fraction and the electronic partial width at the 90% confidence level are provided.

Physics↗
DOE OSTI2025

Entanglement Cost for Infinite-Dimensional Physical Systems

We prove that the entanglement cost equals the regularized entanglement of formation for any infinite-dimensional quantum state ρ ΑΒ with finite quantum entropy on at least one of the subsystems A or B. This generalizes a foundational result in quantum information theory that was previously formulated only for operations and states on finite-dimensional systems. The extension to infinite-dimensional systems is nontrivial because the conventional tools for establishing both the direct and converse bounds, i.e., strong typicality, monotonicity, and asymptotic continuity, are no longer directly applicable. To address this problem, we construct a new entanglement dilution protocol for infinite-dimensional states implementable by local operations and a finite amount of one-way classical communication (one-way LOCC), using weak and strong typicality multiple times. We also prove the optimality of this protocol among all protocols, even under infinite-dimensional separable operations, by developing an argument based on alternative forms of monotonicity and asymptotic continuity of the entanglement of formation for infinite-dimensional states. Along the way, we derive a new integral representation for the quantum entropy of infinite-dimensional states, which we believe to be of independent interest. Our results allow us to fully characterize an important operational entanglement measure—the entanglement cost—for all infinite-dimensional physical systems.

Complexity↗
DOE OSTI2024

The impact of low-mode symmetry on inertial fusion energy output in the burning plasma state

Indirect Drive Inertial Confinement Fusion Experiments on the National Ignition Facility (NIF) have achieved a burning plasma state with neutron yields exceeding 170 kJ, roughly 3 times the prior record and a necessary stage for igniting plasmas. The results are achieved despite multiple sources of degradations that lead to high variability in performance. Results shown here, for the first time, include an empirical correction factor for mode-2 asymmetry in the burning plasma regime in addition to previously determined corrections for radiative mix and mode-1. Analysis shows that including these three corrections alone accounts for the measured fusion performance variability in the two highest performing experimental campaigns on the NIF to within error. Here we quantify the performance sensitivity to mode-2 symmetry in the burning plasma regime and apply the results, in the form of an empirical correction to a 1D performance model. Furthermore, we find the sensitivity to mode-2 determined through a series of integrated 2D radiation hydrodynamic simulations to be consistent with the experimentally determined sensitivity only when including alpha-heating.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

A new method for solving the linearized 1D Vlasov–Poisson system yielding a new class of solutions

We describe a new method for solving the linearized 1D Vlasov–Poisson system by using properties of Cauchy-type integrals. Our method remedies critical flaws of the two standard methods, reveals a previously unrecognized Gaussian-in-time-like decay, and can also account for an externally applied electric field. The Landau approximation involves deforming the Bromwich contour around the poles closest to the real axis due to the analytically continued dielectric function, finding the long-time behavior for a stable system: Landau damping. Jackson's generalization encircles all poles while sending the contour to infinity, assuming its contribution vanishes, which is not true in general. This gives incorrect solutions for physically reasonable configurations and can exhibit pathological behavior, of which we show examples. The van Kampen method expresses the solution for a stable equilibrium as a continuous superposition of waves, resulting in an opaque integral. Case's generalization includes unstable systems and predicts a decaying discrete mode for each growing discrete mode, an apparent contradiction to both the Jackson solution and ours. We show, without imposing additional constraints, that the decaying modes are never present in the time evolution due to an exact cancellation with part of the continuum. Our solution is free of integral expressions, is obtained using algebra and Laurent series expansions, does not rely on analytic continuations, and results in a correct asymptotically convergent form in the case of infinite sums. The analysis used can be readily applied in higher-dimensional, electromagnetic systems and also provides a new technique for evaluating certain inverse Laplace transforms.

Physics↗
DOE OSTI2025

Crystal structure and catalytic mechanism of drimenol synthase, an unusual bifunctional terpene cyclase–phosphatase

Drimenol synthase fromAquimarina spongiae(AsDMS) is a highly unusual chimera that integrates two distinct, sequential isoprenoid processing activities within a single polypeptide chain. AsDMS catalyzes the class II cyclization of farnesyl diphosphate (FPP) to form drimenyl diphosphate, which then undergoes enzyme-catalyzed hydrolysis to yield drimenol, a bioactive sesquiterpene alcohol with antifungal and anticancer properties. Here, we report the X-ray crystal structures of AsDMS and its complex with a sesquiterpene thiol. The AsDMS structure exhibits a didomain architecture consisting of a terpene cyclase β domain and a haloacid dehalogenase-like phosphatase domain, with two distinct active sites located on opposite sides of the protein. Mechanistic studies show that dephosphorylation of the drimenyl diphosphate intermediate proceeds through stepwise hydrolysis such that two equivalents of inorganic phosphate rather than inorganic pyrophosphate are coproducts of the reaction sequence. When the AsDMS reaction is performed in H 2 18 O, 18 O is not incorporated into drimenol, indicating that the hydroxyl oxygen of drimenol originates from the prenyl oxygen of FPP rather than a water molecule from bulk solution. These results correct a mechanistic proposal previously advanced by another group. Surprisingly, AsDMS exhibits substrate promiscuity, catalyzing the conversion of the slowly reactive substrate mimic farnesyl-S-thiolodiphosphate into cyclic and linear sesquiterpene products. Structural and mechanistic insights gained from AsDMS illustrate the functional diversity of terpene biosynthetic enzymes and provide a foundation for engineering “designer cyclase” assemblies capable of generating a wide variety of terpenoid products.

Science & Technology - Other Topics↗
DOE OSTI2022

Spectral form factor of a quantum spin glass

It is widely expected that systems which fully thermalize are chaotic in the sense of exhibiting random-matrix statistics of their energy level spacings, whereas integrable systems exhibit Poissonian statistics. In this paper, we investigate a third class: spin glasses. These systems are partially chaotic but do not achieve full thermalization due to large free energy barriers. We examine the level spacing statistics of a canonical infinite-range quantum spin glass, the quantum p-spherical model, using an analytic path integral approach. We find statistics consistent with a direct sum of independent random matrices, and show that the number of such matrices is equal to the number of distinct metastable configurations — the exponential of the spin glass “complexity” as obtained from the quantum Thouless-Anderson-Palmer equations. We also consider the statistical properties of the complexity itself and identify a set of contributions to the path integral which suggest a Poissonian distribution for the number of metastable configurations. Our results show that level spacing statistics can probe the ergodicity-breaking in quantum spin glasses and provide a way to generalize the notion of spin glass complexity beyond models with a semi-classical limit.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Developing Separate Effects Transient Test Experiments Using an Out-of-Pile Flowing Water Loop

In 2017 the Transient Reactor Test Facility was restarted after being placed in a standby state since 1994. This Test Reactor’s restart has since enabled the progressive development of new nuclear technologies within the U.S. that were previously required to outsource to other countries. While the reactor’s restart was a large feat worthy of recognition, the experimental use of its characteristics has required the further development of in-pile experimental infrastructure sufficient to support programmatic needs. This hardware have taken the form of capsule designs (compact and elongated) as well as loop concepts representing the phenomena of interest for a subset of separate effects tests desire for each respective testing campaign. The Transient Testing Program has a large-integrated effort that aligns with the U.S. Department of Energy’s current needs. This study compliments those programmatic elements by developing, fabricating and demonstrating a full-scale flowing water loop in an out-of-pile environment. The goal of this effort is to develop a pragmatic understanding of the engineering capabilities and limitations associated with geometric form-factors, metering technology, and controls logic under representative thermal hydraulic conditions that would be experienced within the TREAT reactor during an in-pile reactivity initiated accident test. The outcomes of this study result in an evaluation of the conceptual design of a comprehensive flowing water loop including objective figures of merit (FoMs) for comparing unique instrumentation and the basis for their selection during operations. These efforts directly contribute to and are required for the further advancement of transient testing capabilities within the U.S.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2022

Neural Networks for Nuclear Reactions in MAESTROeX

We demonstrate the use of neural networks to accelerate the reaction steps in the MAESTROeX stellar hydrodynamics code. A traditional MAESTROeX simulation uses a stiff ODE integrator for the reactions; here, we employ a ResNet architecture and describe details relating to the architecture, training, and validation of our networks. Our customized approach includes options for the form of the loss functions, a demonstration that the use of parallel neural networks leads to increased accuracy, and a description of a perturbational approach in the training step that robustifies the model. We test our approach on millimeter-scale flames using a single-step, 3-isotope network describing the first stages of carbon fusion occurring in Type Ia supernovae. We train the neural networks using simulation data from a standard MAESTROeX simulation, and show that the resulting model can be effectively applied to different flame configurations. This work lays the groundwork for more complex networks, and iterative time-integration strategies that can leverage the efficiency of the neural networks.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Spherical trihedral metallo-borospherenes

The discovery of borospherenes unveiled the capacity of boron to form fullerene-like cage structures. While fullerenes are known to entrap metal atoms to form endohedral metallofullerenes, few metal atoms have been observed to be part of the fullerene cages. Here we report the observation of a class of remarkable metallo-borospherenes, where metal atoms are integral parts of the cage surface. We have produced La 3 B 18 - and Tb 3 B 18 - and probed their structures and bonding using photoelectron spectroscopy and theoretical calculations. Global minimum searches revealed that the most stable structures of Ln 3 B 18 - are hollow cages with D 3h symmetry. The B 18 -framework in the Ln 3 B 18 - cages can be viewed as consisting of two triangular B6 motifs connected by three B 2 units, forming three shared B 10 rings which are coordinated to the three Ln atoms on the cage surface. These metallo-borospherenes represent a new class of unusual geometry that has not been observed in chemistry heretofore.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Leveraging Existing Assets for Long Duration Energy Storage

Increased renewables penetration to electrical grid is necessary to reduce overall emissions from the electrical power generation sector. Nonetheless, its integration creates challenges to grid operators who must match the power being generated by intermittent renewables and other traditional energy sources with the demand from consumers, while ensuring the reliability and power quality for the entire system. Energy storage has been proposed as an alternative to natural gas peaking plants and a form to deliver excess renewable energy generation at times of peak demand. For energy storage to provide benefits to end customers (energy consumers), it must be reliable, efficient, and cost effective. The Illinois Sustainable Technology Center (ISTC), one of the surveys that integrate the Prairie Research Institute (PRI), aims to develop a Center for Energy Storage at Existing Assets (CESEA) at UIUC with the participation of Waste Pressure Corp and Ecotek Engineering USA LLC. CESEA will focus on LDES systems that can integrate to existing infrastructure in a manner that reduces the initial capital expenditure and demonstrates the ability to repurpose fossil assets that would otherwise become stranded, to serve the energy transition. CESEA aims to leverage UIUC’s unique facilities to validate LDES systems performance at a relevant operating environment. UIUC’s facilities include a 85-MW combined heat and power (CHP) power plant, two (2) solar PV plants totaling over 18 MWdc of installed capacity, an electrical grid along with a substation at transmission and distribution voltages, a 22-mile gas pipeline network operating at two pressure levels, along with steam and chilled water distribution networks. The new LDES systems will connect to the existing UIUC grid through a new test electrical station, which will have the capacity to accommodate additional connections to test new devices and technologies as part of future CESEA R&D activities. The test electrical station will contain meters, instrumentation, and controls to accurately capture data and allow optimization of control algorithms. CESEA will initially focus on technologies that: i) utilize existing equipment or facilities to perform at least one of the process steps in LDES (charging, storage, or discharging), ii) leverage mature or commercially available components or controls, iii) show potential for cost-leadership in 10+ hour storage at a commercial scale. Initial technologies that were identified to meet these criteria include Compressed Gas Energy Storage (CGES), and TES. CGES stores electricity by raising the pressure of a compressible gas inside a control volume and converting the stored energy to electricity via expansion-generation. CGES is a generalization of CAES that covers any working gas (not just air). A successful CGES demo will help to circumvent many challenges faced by CAES (long development times due to site prospecting, high cost of compression and storage, heat recovery management, etc.) by: 1) utilizing existing infrastructure (compressors, pipelines, underground storage or pressure vessels) used in the transportation and storage of industrial gases for LDES charging and storage; 2) deploying over sites already-developed for industrial applications with minor additional work; 3) leveraging the price structure of commercial industrial gas to cover the costs of electricity used during charging. A previous DOE-sponsored conceptual study (DE-FE-0032018) estimated the levelized cost of energy of a 1.1 MW / 17 MWh CGES system at $0.08/kWh, with a commercial 10x scale system cost estimated at <$0.04/kWh (Giardinella, 2022). The pilot-sized system was estimated to avoid up to 2693 tons of CO2/year.

25 ENERGY STORAGE↗
DOE OSTI2025

Virtual Self-Excited Induction Generator-Based Grid-Forming Inverter Control for Robust Voltage Regulation Under Nonideal Loading

This paper presents a generator-inspired control methodology for grid-forming (GFM) inverters that deliberately emulates a self-excited induction generator so that the inverter can hold its voltage and frequency under difficult loading and severe terminal disturbances across wide voltage and frequency ranges. The design integrates a Lyapunov energy function-based inner loop to provide high bandwidth and strong disturbance rejection, and it complements this with a passivity-based argument that furnishes a coherent large-signal stability guarantee beyond small-signal limits. Analytical insights are developed via the Krylov-Bogoliubov-Mitropolsky averaging method, which reveals an intrinsic resistive droop characteristic; these closed-form relations both explain the observed dynamics and yield simple, decentralized tuning rules. The methodology is validated on a controller-hardware-in-the-loop platform and exercised in real time across balanced, unbalanced, and nonlinear loads, as well as during parallel operation. Across these scenarios, the inverter maintains balanced three-phase voltages, limits harmonic content, settles quickly with well-damped transients, and remains resilient when multiple units operate in parallel. The contributions are a self-excited-machine-inspired GFM controller with enhanced dynamic performance and robustness, a single stability rationale grounded in passivity, closed-form expressions that guide tuning, and comprehensive hardware-in-the-loop validations demonstrating effectiveness and superiority under challenging operating conditions.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Resolved resonance region evaluations of n+ 206,207,208 Pb for fast spectrum applications

Resolved resonance region evaluations of the major isotopes of natural lead, 206 Pb, 207 Pb, 208 Pb, have been per formed to support the development of Generation IV reactors. In this study, validation of nuclear data for lead fast reactors was performed with simulations of shielding benchmarks, integral critical benchmarks, and quasi-differential scattering measurements. Sensitivity analyses of these systems showed that elastic scattering reactions above 100 keV were the dominant reactions driving system performance. The resolved resonance regions (RRRs) of the lead isotopes extend past 100 keV, making the RRR an ideal starting point to evaluate lead cross sections. Since the R-matrix requires knowledge of bound, distant, and observed resonances, it was necessary to evaluate from 10 -5 eV up to the respective limit of the RRR. The 208 Pb RRR evaluation was extended to 1.5 MeV in order to obtain resonance parameters used to calculate new elastic scattering angular distributions up to 1.5 MeV. Resonance parameter uncertainties and covariance were generated using the R-matrix code SAMMY. The new RRR parameters show a direct improvement to the scattering kernel below 1.5 MeV which in turn greatly improves fast critical experiments over ENDF/B-VIII.0.

206Pb↗
DOE OSTI2024

Loops of loops expansion in the amplituhedron

We study a novel geometric expansion for scattering amplitudes in the planar sector of $\mathcal{N}$ = 4 super Yang-Mills theory, in the context of the Amplituhedron which reproduces the all-loop integrand as a canonical differential form on the positive geometry. In a paper by Arkani-Hamed, Henn and one of the authors, it was shown that this result can be recast in terms of negative geometries with a certain hierarchy of loops (closed cycles) in the space of loop momenta, represented by lines in momentum twistor space. One can then calculate an all-loop order result in the approximation where only tree graphs in the space of all loops are considered. Furthermore, using differential equation methods, it is possible to calculate and resum integrated expressions and obtain strong coupling results. In this paper, we provide a more general framework for the ‘loops of loops’ expansion and outline a powerful method for the determination of differential forms for higher-order geometries. We solve the problem completely for graphs with one internal cycle, but the method can be used more generally for other geometries.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Measurement of the e + e − → Λ Σ ¯ 0 + c . c . cross sections at s from 2.3094 to 3.0800 GeV

The Born cross sections and effective form factors of the process e + e − → Λ Σ ¯ 0 + c . c . are measured at 14 center-of-mass energy points from 2.3094 to 3.0800 GeV, based on data corresponding to an integrated luminosity of ( 478.5 ± 4.8 ) pb − 1 collected with the BESIII detector. A nonzero Born cross section is observed at the center-of-mass energy of 2.3094 GeV with a statistical significance of more than five standard deviations, and the cross sections at other energies are obtained with improved precision compared to earlier measurements from the Collaboration. The Born cross-section line shape is described better by a shape considering the strong-interaction effects than by a pQCD motivated functional form. Published by the American Physical Society 2024

Astronomy & Astrophysics↗
DOE OSTI2026

Dual Representations and H ∞ -Optimal Control of Partial Differential Equations

We consider H ∞ -optimal state-feedback control of the class of linear Partial Differential Equations (PDEs) which admit a Partial Integral Equation (PIE) representation. While linear matrix inequalities are commonly used for optimal control of Ordinary Differential Equations (ODEs), the absence of a universal state-space representation and suitable dual form prevents such methods from being applied to optimal control of PDEs. Specifically, for ODEs, the controller synthesis problem is defined in state-space, and duality is used to resolve the bilinearity of that synthesis problem. Recently, the PIE representation was proposed as a universal state-space representation for linear PDE systems. In this paper, we show that any PDE system represented by a PIE admits a dual PIE with identical stability and I/O properties. This result allows us to reformulate the stabilizing and optimal state-feedback control problems as convex optimization over the cone of positive Partial Integral (PI) operators. Operator inversion formulae then allow us to construct feedback gains for the original PDE system. The results are verified through application to several canonical problems in optimal control of PDEs and indicate the resulting bounds on H ∞ norm are not conservative.

42 ENGINEERING↗