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All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

A methodology based on reduced complexity algorithm for system applications using microprocessors

The paper considers a methodology on the analysis and design of a minimum mean-square error criterion linear system incorporating a tapped delay line (TDL) where all the full-precision multiplications in the TDL are constrained to be powers of two. A linear equalizer based on the dispersive and additive noise channel is presented. This microprocessor implementation with optimized power of two TDL coefficients achieves a system performance comparable to the optimum linear equalization with full-precision multiplications for an input data rate of 300 baud.

Yan, T. Y.↗
NASA NTRS1989

An algorithm for the solution of dynamic linear programs

The algorithm's objective is to efficiently solve Dynamic Linear Programs (DLP) by taking advantage of their special staircase structure. This algorithm constitutes a stepping stone to an improved algorithm for solving Dynamic Quadratic Programs, which, in turn, would make the nonlinear programming method of Successive Quadratic Programs more practical for solving trajectory optimization problems. The ultimate goal is to being trajectory optimization solution speeds into the realm of real-time control. The algorithm exploits the staircase nature of the large constraint matrix of the equality-constrained DLPs encountered when solving inequality-constrained DLPs by an active set approach. A numerically-stable, staircase QL factorization of the staircase constraint matrix is carried out starting from its last rows and columns. The resulting recursion is like the time-varying Riccati equation from multi-stage LQR theory. The resulting factorization increases the efficiency of all of the typical LP solution operations over that of a dense matrix LP code. At the same time numerical stability is ensured. The algorithm also takes advantage of dynamic programming ideas about the cost-to-go by relaxing active pseudo constraints in a backwards sweeping process. This further decreases the cost per update of the LP rank-1 updating procedure, although it may result in more changes of the active set that if pseudo constraints were relaxed in a non-stagewise fashion. The usual stability of closed-loop Linear/Quadratic optimally-controlled systems, if it carries over to strictly linear cost functions, implies that the saving due to reduced factor update effort may outweigh the cost of an increased number of updates. An aerospace example is presented in which a ground-to-ground rocket's distance is maximized. This example demonstrates the applicability of this class of algorithms to aerospace guidance. It also sheds light on the efficacy of the proposed pseudo constraint relaxation scheme.

Psiaki, Mark L.↗
DOE OSTI2015

Determination of the optimal tolerance for MLC positioning in sliding window and VMAT techniques

Purpose: Several authors have recommended a 2 mm tolerance for multileaf collimator (MLC) positioning in sliding window treatments. In volumetric modulated arc therapy (VMAT) treatments, however, the optimal tolerance for MLC positioning remains unknown. In this paper, the authors present the results of a multicenter study to determine the optimal tolerance for both techniques. Methods: The procedure used is based on dynalog file analysis. The study was carried out using seven Varian linear accelerators from five different centers. Dynalogs were collected from over 100 000 clinical treatments and in-house software was used to compute the number of tolerance faults as a function of the user-defined tolerance. Thus, the optimal value for this tolerance, defined as the lowest achievable value, was investigated. Results: Dynalog files accurately predict the number of tolerance faults as a function of the tolerance value, especially for low fault incidences. All MLCs behaved similarly and the Millennium120 and the HD120 models yielded comparable results. In sliding window techniques, the number of beams with an incidence of hold-offs >1% rapidly decreases for a tolerance of 1.5 mm. In VMAT techniques, the number of tolerance faults sharply drops for tolerances around 2 mm. For a tolerance of 2.5 mm, less than 0.1% of the VMAT arcs presented tolerance faults. Conclusions: Dynalog analysis provides a feasible method for investigating the optimal tolerance for MLC positioning in dynamic fields. In sliding window treatments, the tolerance of 2 mm was found to be adequate, although it can be reduced to 1.5 mm. In VMAT treatments, the typically used 5 mm tolerance is excessively high. Instead, a tolerance of 2.5 mm is recommended.

07 ISOTOPE AND RADIATION SOURCES↗
DOE OSTI2014

Finite Energy and Bounded Attacks on Control System Sensor Signals

Control system networks are increasingly being connected to enterprise level networks. These connections leave critical industrial controls systems vulnerable to cyber-attacks. Most of the effort in protecting these cyber-physical systems (CPS) has been in securing the networks using information security techniques and protection and reliability concerns at the control system level against random hardware and software failures. However, besides these failures the inability of information security techniques to protect against all intrusions means that the control system must be resilient to various signal attacks for which new analysis and detection methods need to be developed. In this paper, sensor signal attacks are analyzed for observer-based controlled systems. The threat surface for sensor signal attacks is subdivided into denial of service, finite energy, and bounded attacks. In particular, the error signals between states of attack free systems and systems subject to these attacks are quantified. Optimal sensor and actuator signal attacks for the finite and infinite horizon linear quadratic (LQ) control in terms of maximizing the corresponding cost functions are computed. The closed-loop system under optimal signal attacks are provided. Illustrative numerical examples are provided together with an application to a power network with distributed LQ controllers.

Cyber-physical↗
DOE OSTI2016

Multigrid Reduction in Time for Nonlinear Parabolic Problems

The need for parallel-in-time is being driven by changes in computer architectures, where future speed-ups will be available through greater concurrency, but not faster clock speeds, which are stagnant.This leads to a bottleneck for sequential time marching schemes, because they lack parallelism in the time dimension. Multigrid Reduction in Time (MGRIT) is an iterative procedure that allows for temporal parallelism by utilizing multigrid reduction techniques and a multilevel hierarchy of coarse time grids. MGRIT has been shown to be effective for linear problems, with speedups of up to 50 times. The goal of this work is the efficient solution of nonlinear problems with MGRIT, where efficient is defined as achieving similar performance when compared to a corresponding linear problem. As our benchmark, we use the p-Laplacian, where p = 4 corresponds to a well-known nonlinear diffusion equation and p = 2 corresponds to our benchmark linear diffusion problem. When considering linear problems and implicit methods, the use of optimal spatial solvers such as spatial multigrid imply that the cost of one time step evaluation is fixed across temporal levels, which have a large variation in time step sizes. This is not the case for nonlinear problems, where the work required increases dramatically on coarser time grids, where relatively large time steps lead to worse conditioned nonlinear solves and increased nonlinear iteration counts per time step evaluation. This is the key difficulty explored by this paper. We show that by using a variety of strategies, most importantly, spatial coarsening and an alternate initial guess to the nonlinear time-step solver, we can reduce the work per time step evaluation over all temporal levels to a range similar with the corresponding linear problem. This allows for parallel scaling behavior comparable to the corresponding linear problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2015

Finite Energy and Bounded Actuator Attacks on Cyber-Physical Systems

As control system networks are being connected to enterprise level networks for remote monitoring, operation, and system-wide performance optimization, these same connections are providing vulnerabilities that can be exploited by malicious actors for attack, financial gain, and theft of intellectual property. Much effort in cyber-physical system (CPS) protection has focused on protecting the borders of the system through traditional information security techniques. Less effort has been applied to the protection of cyber-physical systems from intelligent attacks launched after an attacker has defeated the information security protections to gain access to the control system. In this paper, attacks on actuator signals are analyzed from a system theoretic context. The threat surface is classified into finite energy and bounded attacks. These two broad classes encompass a large range of potential attacks. The effect of theses attacks on a linear quadratic (LQ) control are analyzed, and the optimal actuator attacks for both finite and infinite horizon LQ control are derived, therefore the worst case attack signals are obtained. The closed-loop system under the optimal attack signals is given and a numerical example illustrating the effect of an optimal bounded attack is provided.

Djouadi, Seddik M↗
DOE OSTI2015

A feasibility study: Selection of a personalized radiotherapy fractionation schedule using spatiotemporal optimization

Purpose: To investigate the impact of using spatiotemporal optimization, i.e., intensity-modulated spatial optimization followed by fractionation schedule optimization, to select the patient-specific fractionation schedule that maximizes the tumor biologically equivalent dose (BED) under dose constraints for multiple organs-at-risk (OARs). Methods: Spatiotemporal optimization was applied to a variety of lung tumors in a phantom geometry using a range of tumor sizes and locations. The optimal fractionation schedule for a patient using the linear-quadratic cell survival model depends on the tumor and OAR sensitivity to fraction size (α/β), the effective tumor doubling time (T{sub d}), and the size and location of tumor target relative to one or more OARs (dose distribution). The authors used a spatiotemporal optimization method to identify the optimal number of fractions N that maximizes the 3D tumor BED distribution for 16 lung phantom cases. The selection of the optimal fractionation schedule used equivalent (30-fraction) OAR constraints for the heart (D{sub mean} ≤ 45 Gy), lungs (D{sub mean} ≤ 20 Gy), cord (D{sub max} ≤ 45 Gy), esophagus (D{sub max} ≤ 63 Gy), and unspecified tissues (D{sub 05} ≤ 60 Gy). To assess plan quality, the authors compared the minimum, mean, maximum, and D{sub 95} of tumor BED, as well as the equivalent uniform dose (EUD) for optimized plans to conventional intensity-modulated radiation therapy plans prescribing 60 Gy in 30 fractions. A sensitivity analysis was performed to assess the effects of T{sub d} (3–100 days), tumor lag-time (T{sub k} = 0–10 days), and the size of tumors on optimal fractionation schedule. Results: Using an α/β ratio of 10 Gy, the average values of tumor max, min, mean BED, and D{sub 95} were up to 19%, 21%, 20%, and 19% larger than those from conventional prescription, depending on T{sub d} and T{sub k} used. Tumor EUD was up to 17% larger than the conventional prescription. For fast proliferating tumors with T{sub d} less than 10 days, there was no significant increase in tumor BED but the treatment course could be shortened without a loss in tumor BED. The improvement in the tumor mean BED was more pronounced with smaller tumors (p-value = 0.08). Conclusions: Spatiotemporal optimization of patient plans has the potential to significantly improve local tumor control (larger BED/EUD) of patients with a favorable geometry, such as smaller tumors with larger distances between the tumor target and nearby OAR. In patients with a less favorable geometry and for fast growing tumors, plans optimized using spatiotemporal optimization and conventional (spatial-only) optimization are equivalent (negligible differences in tumor BED/EUD). However, spatiotemporal optimization yields shorter treatment courses than conventional spatial-only optimization. Personalized, spatiotemporal optimization of treatment schedules can increase patient convenience and help with the efficient allocation of clinical resources. Spatiotemporal optimization can also help identify a subset of patients that might benefit from nonconventional (large dose per fraction) treatments that are ineligible for the current practice of stereotactic body radiation therapy.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2020

An Experimental Feasibility Study on Applying Neutron Tomography to Encapsulated Spent Nuclear Fuel - 20050

Visual inspection makes easier to ensure the integrity and safety of spent nuclear fuel (SNF) than any classical techniques. Various classical techniques have been applied but there are no reliable methods to qualitatively and quantitatively verify spent fuel in dry storage. Thus, the present authors have developed the prototype safeguards apparatus for dry storage employing the array of He-4 gas scintillation detectors (S670E, Arktis Radiation Detectors Ltd., Switzerland), newly designed to simultaneously measure thermal and fast neutrons without any moderators. The S670E detector has a cylindrical shape with a diameter of 52 mm and active length of 600 mm (total length: 875 mm). The detector is filled by He-4 gas with an approximate pressure of 180 bar for fast neutron detection, and its inner wall is coated by Li-6 for thermal neutron detection. The scintillation lights generated via Li-6 nuclear reaction and elastic scattering are collected by 24 SiPMs linearly paired at the center of the detector. The detector delivers a TTL (Transistor-Transistor Logic) output for pulse readout and UART (Universal Asynchronous Receiver Transmitter) for device control. In order to assess feasibility of the apparatus, an experimental system has been designed, built, and optimized via computational studies. Cf-252 neutron sources and linearly arrayed detectors, working as a single detector, were occupied for this study due to the difficulties in working with SNF. The laboratory scale cask (diameter: 0.67 m, height: 1.5 m), minimized by a factor of 10 compared to the actual thickness of a commercial TN-32 cask, was also manufactured. The detector array was designed to rotate the lab-scale cask and obtain 36 image profiles at every 10 degrees. All profiles were aligned in single frame image called a sinogram, and the cross-sectional image was then fabricated by the inverse radon transform algorithm. These experiments have been repeated with different configurations and numbers of sources. Some gamma-ray sources were also measured with neutron sources in order to distinguish between neutron and gamma-ray pulses. Basically, a He-4 detector is designed to run on Linux OS so it is difficult to directly apply to Windows-based equipment widely used in S. Korea. Therefore, a new data acquisition board working on Windows OS was designed and built. The board mainly consists of FPGA (Field Programmable Gate Array) and SoC (System on Chip) for TTL pulse readout, sorting measured data, and transferring data to a user interface. In conclusion, the tomographic system at lab-scale has shown considerable potential to detect a partial or gross defect of encapsulated assemblies in dry storage. Next steps of this study will be to 1) repeatedly carry out experiments to demonstrate scientific reliability and validity, and 2) numerically integrate signals with weight factors to enhance the image quality since the suggested system based on passive interrogation method requires longer measurement time. Finally, the system will apply to a commercial dry storage phased out soon in S. Korea. (authors)

07 ISOTOPE AND RADIATION SOURCES↗
NASA NTRSDate not supplied

A Comparison of Control Allocation Methods in the Presence of Parametric Model Uncertainty

When allocating redundant effectors to virtual control commands, linear (generalized inverse) allocators have historically been used on aircraft and spacecraft. While simple to implement, generalized inverses are unable to realize a significant portion of the attainable moments. To address this drawback, the control allocation problem can also be formulated as a linear programming or quadratic programming problem and solved using convex optimization based solvers. These approaches have been shown to access a larger set of attainable moments, however, little work has been done to understand the performance of convex optimization-based control allocation in the presence of parametric model uncertainty. This paper seeks to compare the performance of several control allocation approaches, including two forms of generalized inverse allocators, the pseudo inverse and minimum-variance, and the linear programming and quadratic programming approach in the presence of parametric model uncertainty. The performance of these four allocators were tested on an aircraft model in the presence of realistic parametric model uncertainty and the convex optimization approaches were shown to outperform the generalized inverses.

Luke J Miller↗
NASA NTRS1987

A method for nonlinear optimization with discrete design variables

A numerical method is presented for the solution of nonlinear discrete optimization problems. The applicability of discrete optimization to engineering design is discussed, and several standard structural optimization problems are solved using discrete design variables. The method uses approximation techniques to create subproblems suitable for linear mixed-integer programming methods. The method employs existing software for continuous optimization and integer programming.

Olsen, Gregory R.↗
NASA NTRSDate not supplied

Generalized Linear Targeting For Cislunar Flight

An important element of Artemis and NASA’s campaign to explore the Moon is the autonomous onboard two-level targeter (TLT) used during all cislunar flight phases. The function of the TLT is to autonomously recompute the burn targets for the upcoming burn (or multiple burns) in response to navigation and vehicle dispersion providing a solution that meets all of the trajectory constraints. Although the TLT has been utilized previously as a ground-based planning tool, and flown onboard during the Artemis I mission, it’s complexity and iterative nature make is difficult to incorporate into and support rapid analyses such as robust optimal trajectory design applications where speed is essential. In this paper, a set of generalized linear targeting algorithms that mimics many of the properties of the TLT is derived. The generalized algorithms can handle single or multiple impulsive maneuvers, with multiple constraints at multiple fixed or variable times. A linear targeting algorithm for finite burn maneuvers is also derived. The generalized linear targeting algorithms are exceptionally fast and easy to implement in Monte Carlo analysis, linear covariance (LinCov) analysis, and robust optimal trajectory design. Several cislunar flight examples are provided.

Linear Covariance Analysis↗
DOE OSTI2014

WE-A-BRF-01: Dual-Energy CT Imaging in Diagnostic Imaging and Radiation Therapy

The quantification accuracy of dual-energy imaging is influenced by the fundamentals of x-ray physics, system geometry, data acquisition hardware/protocol, system calibration, and image processing technique. This symposium will provide updates on the following advanced application areas: Mammography. Volumetric breast density techniques based on standard mammograms require estimation of breast thickness, which is difficult to accurately measure. By comparison, calculation of breast density using dual energy mammography does not require measurement of breast thickness. Dual energy mammography has been implemented using both energy integrating flat panel detectors in conjunction with beam energy switching and energy resolved photon counting detectors. These techniques have been optimized using simulation studies and validated using physical phantoms and postmortem breasts. Chemical decomposition was used as the gold standard for volumetric breast density measurement in postmortem breasts. Breast density measurements have also been compared with results from four-category BI-RADS density rankings, standard image thresholding and Fuzzy k-mean clustering techniques. These studies indicate that dual energy mammography can be used to accurately measure volumetric breast density. Cardiovascular CT. The predicative accuracy of risk models for recurrent stroke and cardiac arrest depends heavily on accurate differentiation of thrombus or calcium from iodine in left atrial appendage or coronary arteries. The amount of energy separation is constrained by image noise; therefore, optimal kVp, beam filtration, and balanced flux are essential for the quantification accuracy of iodine and calcium. The basis materials are combined linearly to generate monochromatic energy images, where CT# accuracy and CNR are energy dependent. With optimal monochromatic energy, the mean iodine concentration for the thrombus, circulatory stasis, and control groups are significantly different. Risk classification based on calcium scores shows excellent agreement with classification on the basis of conventional coronary artery calcium scoring. These studies demonstrate dual-energy cardiovascular CT can potentially be a noninvasive and sensitive modality in high risk patients. On-board KV/MV Imaging. To enhance soft tissue contrast and reduce metal artifacts, we have developed a dual-energy CBCT technique and a novel on-board kV/MV imaging technique based on hardware available on modern linear accelerators. We have also evaluated the feasibility of these two techniques in various phantom studies. Optimal techniques (energy, beam filtration, # of overlapping projections, etc) have been investigated with unique calibration procedures, which leads to successful decomposition of imaged material into acrylic-aluminum basis material pair. This enables the synthesis of virtual monochromatic (VM) CBCT images that demonstrate much less beam hardening, significantly reduced metal artifacts, and/or higher soft tissue CNR compared to single-energy CBCT. Adaptive Radiation Therapy. DECT could actually contribute to the area of Dose-Guided Radiation Therapy (or Adaptive Therapy). The application of DECT imaging using 80kV and 140 kV combinations could potentially increase the image quality by reducing the bone or high density material artifacts and also increase the soft tissue contrast by a light contrast agent. The result of this higher contrast / quality images is beneficial for deformable image registration / segmentation algorithm to improve its accuracy hence to make adaptive therapy less time consuming in its recontouring process. The real time re-planning prior to per treatment fraction could become more realistic with this improvement especially in hypofractional SBRT cases. Learning Objectives: Learn recent developments of dual-energy imaging in diagnosis and radiation therapy; Understand the unique clinical problem and required quantification accuracy in each application; Understand the different approaches to optimize dual-energy imaging techniques for different applications.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2015

CERN’s Linac4 H{sup −} sources: Status and operational results

Two volume sources equipped with DESY and CERN plasma generators and a low voltage electron dump were operated at 45 kV in the Linac4 tunnel and on a dedicated test stand. These volume sources delivered approximately 20 mA and ensured the commissioning of the Radio Frequency Quadrupole accelerator and of the first section of the Drift Tube Linac. CERN’s prototype of a cesiated surface source equipped with this electron dump was operated continuously from November 2013 to April 2014 on the ion source test stand and is being commissioned in the Linac4 tunnel. Before cesiation, the prototype conditioned in volume mode provided up to 30 mA H{sup −} beam. Short cesiations, of the order of 10 mg effectively reduced the intensity of co-extracted electrons down to 2 - 8 times the H{sup −} current; this cesiated surface operation mode delivered up to 60 mA H{sup −} beam. An H{sup −} beam of the order of 40 mA was sustained up to four weeks operation with 500 μs pulses at 1.2s spacing. A new extraction was designed to match these beam properties. A copy of BNL’s magnetron produced at CERN was tested at BNL and delivered at 40 kV H{sup −} beam exceeding Linac4’s nominal intensity of 80 mA. In this contribution, the performances, dynamic response to cesiation, stability and availability of these prototypes are described. The needed optimization of the emittance of H{sup −} beam above 40 mA is presented, which requires an evolution of the front end that encompasses implementation of a large ceramic insulator.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

SU-F-T-591: SBRT Treatment of Multiple Extracranial Oligometastases Using a Single-Isocenter with Distinct Optimizations (SIDO)

Purpose: A new development in linac-based intracranial radiosurgery is treatment of multiple targets using single isocenter VMAT, which dramatically reduces treatment time while maintaining high conformality and dose gradient. Our purpose is to translate this technique to extracranial SBRT of oligometastases and address additional challenges such as interplay from motion and setup uncertainties. Methods: We propose SIDO (Single Isocenter with Distinct Optimizations) planning in which all VMAT arcs share an isocenter but each arc treats only one target. Setup uncertainties from rotations and deformations are mitigated by applying a couch translation between VMAT arcs, while interplay is minimized by using dynamic conformal arcs (DCAs) as the starting point for VMAT optimization. We compared SIDO to single (VMAT) and dual (VMAT & DCA) isocenter plans for phantom and patient (N=2) cases. Dose statistics included conformity index (CI), gradient index (GI), and modulation factor (MLC opening & total MU). Finally, we determined likelihood of needing a translational shift between SIDO arcs to correct rotational uncertainties using CBCTs from eleven previous SBRT cases. Results: For phantoms with target separations of 5–15cm, CI was 0.87±0.02, 0.89±0.05, and 0.91±0.02, for SIDO, single, and dual-isocenter VMAT respectively. GI was 6.83±1.0, 7.45±1.0 and 5.94±0.7 respectively. SIDO conformity did not trend with increasing distance between PTVs, while gradient decreased for all planning techniques. Using DCAs as the starting point of VMAT optimization decreased modulation, with a 39.4% reduction in monitor units. SIDO had 4.9% and 39% less MU than single and dual-isocenter VMAT respectively. A translational shift between SIDO arcs would be required in 10–28% of cases due to rotational uncertainties to stay within a 5mm margin, for targets separated by ≥10cm. Conclusion: SIDO for extracranial oligometastases has comparable dosimetry to traditional VMAT with low modulation similar to DCAs. Future work will quantify decrease in dosimetric interplay.

60 APPLIED LIFE SCIENCES↗
NASA NTRS1999

Martian Aerocapture Terminal Point Guidance: A Reference Path Optimization Study

An effective method of terminal point guidance is to employ influence coefficients, which are solved from a set of differential equations adjoint to the linearized perturbations of the equations of motion about a reference trajectory. Hence, to optimize this type of guidance, one must first optimize the reference trajectory that the guidance is based upon. This study concentrates on various methods to optimize a reference trajectory for a Martian aerocapture maneuver, including a parametric analysis and first order gradient method. Resulting reference trajectories were tested in separate 2000 6-DOF Monte Carlo runs, using the Atmospheric Guidance Algorithm Testbed for the Mars Surveyor Program 2001 (MSP '01) Orbiter. These results were compared to an August 1998 study using the same terminal point control guidance algorithm and simulation testbed. Satisfactory improvements over the 1998 study are amply demonstrated.

Ro, Theodore U.↗
DOE OSTI2014

Dynamic implicit 3D adaptive mesh refinement for non-equilibrium radiation diffusion

The time dependent non-equilibrium radiation diffusion equations are important for solving the transport of energy through radiation in optically thick regimes and find applications in several fields including astrophysics and inertial confinement fusion. The associated initial boundary value problems that are encountered often exhibit a wide range of scales in space and time and are extremely challenging to solve. To efficiently and accurately simulate these systems we describe our research on combining techniques that will also find use more broadly for long term time integration of nonlinear multi-physics systems: implicit time integration for efficient long term time integration of stiff multi-physics systems, local control theory based step size control to minimize the required global number of time steps while controlling accuracy, dynamic 3D adaptive mesh refinement (AMR) to minimize memory and computational costs, Jacobian Free Newton–Krylov methods on AMR grids for efficient nonlinear solution, and optimal multilevel preconditioner components that provide level independent solver convergence.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

A Solar-assisted Voltage Optimization Method for Transmission Solar Network Power System

This paper proposes a new formulation and solution algorithm that uses transmission level solar inverters to address the security-constrained optimal power flow (SCOPF) problem. The goal is to stabilize voltage fluctuations in transmission networks in base case and contingency scenarios, by using bulk solar power plant with a minimal number of post-contingency corrections. To achieve this goal, a two-stage volt/var optimization method is proposed to first correct all voltage violations with the volt-var alternating current optimal power flow (ACOPF) algorithm for a base case. Then a linearized SCOPF volt-var control algorithm is proposed to identify the corrective actions for all potential voltage violations in all contingency scenarios. The proposed method was tested and validated on a modified IEEE 118-bus system with solar photovoltaic (PV) data.

Photovoltaic, Volt/Var Control↗
NASA NTRS1990

Optimal orbital rendezvous using high and low thrust

Optimal control theory is used to examine a specific class of spacecraft trajectory problems where high- and low-thrust propulsion systems are utilized. These problems assume a spacecraft is in an established orbit about a planet. It is desired to execute an intercept of a pre-determined position in space in a specified amount of time using an optimal high-thrust program. The spacecraft then returns to the original orbit station using the low-thrust propulsion system in an optimal fashion. A minimum fuel solution is sought using the linearized equations of motion, known as the CW equations, which simplify the necessary computations. Solutions are obtained for problems with a fixed final time. However, for the time-open case, the optimal solution is for the final time to be infinite. With a weighted function of the final time in the performance index, a limited range of optimal single impulse solutions for the time -open case can also be found.

Prussing, John E.↗