Search NASA⌕ Search

SEARCH · Search NASA

Results for “Relative Trajectory Cost”

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 91 records · Page 5

Benefits of high aerodynamic efficiency to orbital transfer vehicles

The benefits and costs of high aerodynamic efficiency on aeroassisted orbital transfer vehicles (AOTV) are analyzed. Results show that a high lift to drag (L/D) AOTV can achieve significant velocity savings relative to low L/D aerobraked OTV's when traveling round trip between low Earth orbits (LEO) and alternate orbits as high as geosynchronous Earth orbit (GEO). Trajectory analysis is used to show the impact of thermal protection system technology and the importance of lift loading coefficient on vehicle performance. The possible improvements in AOTV subsystem technologies are assessed and their impact on vehicle inert weight and performance noted. Finally, the performance of high L/D AOTV concepts is compared with the performances of low L/D aeroassisted and all propulsive OTV concepts to assess the benefits of aerodynamic efficiency on this class of vehicle.

Andrews, D. G.↗

Modern Aerocapture Guidance to Enable Reduced-Lift Vehicles at Neptune

Aerocapture is covered extensively in the literature as means of achieving orbital insertion with dramatic mass-saving results compared to fully-propulsive systems. One of the primary obstacles facing aerocapture is the inherent uncertainty associated with passing through a planet’s upper atmosphere. In-flight dispersions due to delivery errors, environment variables, and aerodynamic performance impose a large flight envelope. System studies for aerocapture often select high lift-to-drag ratios to compensate for these uncertainties. However, modern predictor-corrector guidance strategies have shown promise in recent years to provide robust control schemes in-situ. These algorithms do not rely on a pre-calculated reference trajectory and instead employ a numerical optimizer to continuously solve nonlinear equations of motion each guidance cycle. Numerical predictor-corrector strategies may provide considerable accuracy over heritage guidance schemes. The goal of this study is reproduce a landmark study of Neptune aerocapture and apply modern guidance to illustrate relative performance improvements and cost-saving potential. Capture constraints based on the theoretical corridor width are considered. Results indicate that heritage vehicles with moderate lift-to-drag ratios, lower than previous studies have indicated, may prove viable for aerocapture at Neptune.

Heidrich, C. R.↗

Thermal Management Design for the X-33 Lifting Body

The X-33 Advantage Technology Demonstrator offers a rare and exciting opportunity in Thermal Protection System development. The experimental program incorporates the latest design innovation in re-useable, low life cycle cost, and highly dependable Thermal Protection materials and constructions into both ground based and flight test vehicle validations. The unique attributes of the X-33 demonstrator for design application validation for the full scale Reusable Launch Vehicle, (RLV), are represented by both the configuration of the stand-off aeroshell, and the extreme exposures of sub-orbital hypersonic re-entry simulation. There are several challenges of producing a sub-orbital prototype demonstrator of Single Stage to Orbit/Reusable Launch Vehicle (SSTO/RLV) operations. An aggressive schedule with budgetary constraints precludes the opportunity for an extensive verification and qualification program of vehicle flight hardware. However, taking advantage of off the shelf components with proven technologies reduces some of the requirements for additional testing. The effects of scale on thermal heating rates must also be taken into account during trajectory design and analysis. Described in this document are the unique Thermal Protection System (TPS) design opportunities that are available with the lifting body configuration of the X-33. The two principal objectives for the TPS are to shield the primary airframe structure from excessive thermal loads and to provide an aerodynamic mold line surface. With the relatively benign aeroheating capability of the lifting body, an integrated stand-off aeroshell design with minimal weight and reduced procurement and operational costs is allowed. This paper summarizes the design objectives of the X-33 TPS, the flight test requirements driven configuration, and design benefits. Comparisons are made of the X-33 flight profiles and Space Shuttle Orbiter, and lifting body Reusable Launch Vehicle aerothermal environments. The X-33 TPS is based on a design to cost configuration concept. Only RLV critical technologies are verified to conform to cost and schedule restrictions. The one-off prototype vehicle configuration has evolved to minimize the tooling costs by reducing the number of unique components. Low cost approaches such as a composite/blanket leeward aeroshell and the use of Shuttle technology are implemented where applicable. The success of the X-33 will overcome the ballistic re-entry TPS mindset. The X-33 TPS is tailored to an aircraft type mission while maintaining sufficient operational margins. The flight test program for the X-33 will demonstrate that TPS for the RLV is not simply a surface insulation but rather an integrated aeroshell system.

Bouslog, S.↗

The INSTEP Monitoring Network: Merging High-and-Low Cost Measurements to Characterize California Wildfires

Despite challenges with data quality and scope, low-cost sensor networks have skyrocketed in popularity over the last 15 years, making air quality data available on refined spatial scales. More recently, studies have leveraged both high and low-quality instruments to create stronger “hybrid” models, with most studies focusing on particulate matter. Low-cost measurements typically represent ground-level emissions only, providing context for human health issues from climate change-driven events such as wildfires. Since low-cost sensors’ capabilities are localized, daily events and microclimates tend to dominate the data rather than larger regional or atmospheric trends. Likewise, their low cost explains their high uncertainty. In contrast, some regulatory-grade instruments produce column measurements as well, providing reliable information on a broader scope. To bridge this gap while expanding into gas-phase measurements, we deployed 12 air quality sensor packages in California, USA during the 2022 wildfire season. These INSTEP (Inexpensive Network Sensor Technology Exploring Pollution) monitors measure carbon monoxide (CO), carbon dioxide (CO2), ozone (O3), nitrogen dioxide (NO2), and several hydrocarbons including methane (CH4) and formaldehyde (HCHO). Half of the monitors were co-located with remote sensing spectrometers: NASA Pandora and Total Column Carbon Observing Network (TCCON). The overlap in pollutants includes NO2, O3, and HCHO between the INSTEP monitors and the Pandora column measurements. TCCON covers column CO, CO2, and CH4, rounding out our comparison. Most of the monitors were distributed throughout the San Francisco Bay area, and an additional three were located within 100 km of Los Angeles. The sites ranged in geographic and population characteristics, including desert, mountainous, coastal, and urban locations. Since varying environmental conditions such as temperature and pressure are known to challenge sensor performance, we will apply newer sensor “calibration” techniques meant to combat this. We will normalize our sensor signals by z-scoring them prior to applying a single calibration model in the form of multivariate linear regression or an artificial neural network. While this technique has been validated for the hydrocarbon and ozone sensor types (metal oxide), it has not yet been tested on electrochemical and non-dispersive infrared sensors, which are also used in the INSTEP monitors. This will serve as a test to see if this normalization technique – or another – is most effective in accounting for environmental differences among sensors. Related data analysis efforts have found success with a variety of geospatial analysis techniques, including weighted network models in which high-quality instruments are given higher weights than their low-cost counterparts. Our preliminary analysis will focus on kriging, which uses a Gaussian algorithm to assign weights, providing estimated pollution levels at locations between monitors. Smoke trajectory and evolution will also be considered using both measurement types. We also aim to baseline subtract our emission estimates from each region to determine which portion of emissions are regional and local, further characterizing burn differences in northern and southern California fires. Future directions include using INSTEP jointly with TEMPO satellite data, and mobile deployments on aircraft and uncrewed aerial vehicles (UAV).

Low-cost sensors↗

Accelerating room air conditioner efficiency in India: Grid, economic, and policy implications through 2035

India is poised for a rapid surge in space cooling demand, driven by rising incomes, urbanization, and intensifying heat. Between 2025 and 2035, the country is expected to add 130–150 million new room air conditioners (ACs). If Minimum Energy Performance Standards (MEPS) continue to improve at the historical rate of 2–3 % annually, room ACs alone could contribute over 180 GW to peak electricity demand by 2035-nearly 30 % of the projected national total. This study evaluates the impact of an accelerated MEPS trajectory, proposing to raise the 1-star threshold to ISEER 5.0 by 2027, ISEER 6.3 by 2030, and ISEER 7.4 by 2033. Drawing on engineering cost analysis, stock turnover modeling, and retail pricing data, we find that this pathway could reduce peak demand by over 60 GW, save 118 TWh of electricity annually, avoid 49 MtCO₂ of electricity-related emissions per year, avert ₹7.5 trillion (∼US$85 billion) in power system investments, and yield ₹0.7–2.3 trillion (∼US$8–26 billion) in net consumer savings by 2035. Contrary to affordability concerns, empirical trends show that higher efficiency does not increase AC prices. These results highlight the value of ambitious MEPS as a cost-effective strategy for improving grid reliability, reducing emissions, and advancing consumer welfare in emerging economies.

Abhyankar, Nikit↗

3-D multilateration for measurement of earth crustal deformation and network densification

Discussion of how range and range-difference data types can make possible precise three-dimensional measurement of ground station positions and the position of an artificial signal source, without explicit dependence upon the signal source trajectory. An effective strategy for such measurement is to combine the multilateration approach with a VLBI system using natural radio sources. The VLBI methods would provide a coarse grid of three-dimensional benchmark locations on a regional and global scale. Multilateration stations would then occupy these coarse grid locations and provide a means for highly portable, relatively low-cost units to then densify networks on a regional and local scale. Because a multilateration approach can make use of strong artificial radio sources, it makes possible the use of relatively low-cost, highly mobile stations. Such mobile stations are virtually essential for three dimensional surveying in heavily urbanized areas or in rugged terrain.

Ong, K. M.↗

Developing Technology Performance Level Assessments for Early-Stage Wave Energy Converter Technologies: Preprint

The advantage of using Technology Performance Level (TPL) in conjunction with Technology Readiness Level (TRL) assessments in guiding technology development trajectories to successful outcomes in less time, at less overall cost, and with less encountered risk has been well articulated in the literature. In partnership with industry and international collaborators, a TPL assessment methodology for grid-connected applications has been developed through the application of the systems engineering approach. Metrics under seven different categories have been developed, weighted based on their relative relevance, and combined to yield a composite score. The methodology has been implemented in a spreadsheet tool plus a web application specifically aimed at assessing early stage (TRL 1-3) concepts. The target use cases are (a) technology developers improving their design, to find fatal flaws early, to get feedback on current design, to identify areas of improvement that will yield the highest return on investment, (b) reviewers assessing technologies in competitions or for making funding decisions, (c) investor or project developer doing due diligence, (d) policy makers landscaping the technology domain for formulating R&D strategy. The methodology and the tools are undergoing continuous improvement based on the experience and lessons learnt from applying it to internal and external marine energy technology development projects. The methodology is also being adapted for assessing WECs servicing markets outside the continental grid - broadly categorized as Powering the Blue Economy (PBE) applications. Such applications have vastly different functional requirements entailing a modification of the methodology to account for their higher risk tolerance, reduced price sensitivities, lower power needs, different permitting protocols, etc. This paper presents the latest status of the TPL assessment methodology and tools, describes its adaptation to select PBE markets, and explores its extension to other domains where it could provide a comprehensive and holistic measure of a nascent or disruptive technology's technoeconomic performance potential.

metrics↗

Developing Technology Performance Level Assessments for Early-Stage Wave Energy Converter Technologies

The advantage of using Technology Performance Level (TPL) in conjunction with Technology Readiness Level (TRL) assessments in guiding technology development trajectories to successful outcomes in less time, at less overall cost, and with less encountered risk has been well articulated in the literature. In partnership with industry and international collaborators, a TPL assessment methodology for grid-connected applications has been developed through the application of the systems engineering approach. Metrics under seven different categories have been developed, weighted based on their relative relevance, and combined to yield a composite score. The methodology has been implemented in a spreadsheet tool plus a web application specifically aimed at assessing early stage (TRL 1-3) concepts. The target use cases are (a) technology developers improving their design, to find fatal flaws early, to get feedback on current design, to identify areas of improvement that will yield the highest return on investment, (b) reviewers assessing technologies in competitions or for making funding decisions, (c) investor or project developer doing due diligence, (d) policy makers landscaping the technology domain for formulating R&D strategy. The methodology and the tools are undergoing continuous improvement based on the experience and lessons learnt from applying it to internal and external marine energy technology development projects. The methodology is also being adapted for assessing WECs servicing markets outside the continental grid - broadly categorized as Powering the Blue Economy (PBE) applications. Such applications have vastly different functional requirements entailing a modification of the methodology to account for their higher risk tolerance, reduced price sensitivities, lower power needs, different permitting protocols, etc. This paper presents the latest status of the TPL assessment methodology and tools, describes its adaptation to select PBE markets, and explores its extension to other domains where it could provide a comprehensive and holistic measure of a nascent or disruptive technology's technoeconomic performance potential.

metrics↗

Photovoltaic Deployment Scenarios toward Global Decarbonization: Role of Disruptive Technologies

To totally decarbonize global electrical systems using photovoltaics (PVs) in the 2050–2060 decade, the world would need to install 63.4 TW of PV. This article models and explores how a PV manufacturing ramp‐up trajectory toward this goal can be achieved while assuming that investors continue to make financially rational decisions avoiding stranded production assets and therefore protecting their return on investment. The model effectively exploits experience curve benefits in both the scaling of the manufacturing process and continued progress in product design technologies. The scale‐up challenge is amplified because trajectories that achieve this goal require an unprecedented ramp‐up of production capacity over just two decades, followed by relatively modest demand to maintain the installed base and support continued population growth. It is demonstrated that sustainable ramp‐up of manufacturing is indeed possible and shown that the deployment of the requisite manufacturing capacity can be accelerated and accomplished at lower total capital cost by the introduction of disruptive technologies that have lower capital intensity, embedded energy, or higher efficiency.

14 SOLAR ENERGY↗

CubeX: A Compact X-Ray Telescope Enables Both X-Ray Fluorescence Imaging Spectroscopy and Pulsar Timing Based Navigation

This paper describes the benefits of a miniaturized X-ray telescope payload in the context of a lunar mission. The first part describes the payload in detail, the second part summarizes a small satellite mission concept that utilizes its compact form factor and performance. The CubeX instrument can be used for both X-ray fluorescence (XRF) imaging spectroscopy and X-ray pulsar timing based navigation (XNAV). Using our recent technological advances in X-ray optics and sensors, CubeX combines high angular resolution (<1 arcminutes) Miniature Wolter-I X-ray optics (MiXO) with a common focal plane consisting of high spectral resolution (<150 eV at 1 keV) CMOS X-ray sensors and a high timing resolution (< 1 usec) SDD X-ray sensor. This novel combination of the instruments enables both XRF measurements and XNAV operations without moving parts. The high angular resolution of the MiXO opens a wide range of orbital configurations for observation. Given that performance, the instrument has unprecedented small volume (~1×1×6U), mass (<6 kg), and power (<9W) requirements and opens a wide range of applications for a variety of targets and missions including NEOs and Martian moons. In this paper we illustrate one potential application for a lunar mission concept: The elemental composition of the Moon holds keys to understanding the origin and evolution of both the Moon and the Earth. X-ray fluorescence (XRF), induced either by solar X-ray flux or energetic ions, carries decisive signatures of surface elemental composition. X-ray observations, therefore, give a unique, powerful diagnostic tool for remotely determining elemental abundances including major rock forming elements such as Mg, Al, Na, Si, Fe, and Ca. Through high-resolution XRF imaging spectroscopy, CubeX searches for small patches of elusive lower crust and mantle material excavated within and around impact craters. CubeX identifies regional compositional variations and allows straightforward comparison of elemental distributions with the surface topography from LRO and the gravity data from GRAIL. The elemental compositions of the lower crust and the mantle are sensitive to the conditions of the giant impact which led to the Moon's formation and the subsequent lunar magma ocean (LMO), and thus they are key missing pieces in understanding the formation and early evolution of the Moon. In between XRF observations, CubeX also leverages the technology of high resolution X-ray imaging and time series measurements to conduct XNAV operations and evaluate their performance. Deep space navigation is a critical issue for small planetary missions. XNAV can enable low-cost autonomous deep-space navigation, and has the potential to greatly assist, or even outperform, NASA's Deep Space Network (DSN) or ESA's European Space Tracking (ESTRACK). CubeX is designed to perform sequential observations of 3-4 millisecond pulsars (MSPs) to solve the spacecraft trajectory for absolute navigation, and explore the remote sensing capability of XNAV. In the presented mission concept, the Moon's relative proximity enables a straightforward evaluation of the XNAV performance through DSN.

x-ray spectroscopy↗

Multidisciplinary design optimization using genetic algorithms

Multidisciplinary design optimization (MDO) is an important step in the conceptual design and evaluation of launch vehicles since it can have a significant impact on performance and life cycle cost. The objective is to search the system design space to determine values of design variables that optimize the performance characteristic subject to system constraints. Gradient-based optimization routines have been used extensively for aerospace design optimization. However, one limitation of gradient based optimizers is their need for gradient information. Therefore, design problems which include discrete variables can not be studied. Such problems are common in launch vehicle design. For example, the number of engines and material choices must be integer values or assume only a few discrete values. In this study, genetic algorithms are investigated as an approach to MDO problems involving discrete variables and discontinuous domains. Optimization by genetic algorithms (GA) uses a search procedure which is fundamentally different from those gradient based methods. Genetic algorithms seek to find good solutions in an efficient and timely manner rather than finding the best solution. GA are designed to mimic evolutionary selection. A population of candidate designs is evaluated at each iteration, and each individual's probability of reproduction (existence in the next generation) depends on its fitness value (related to the value of the objective function). Progress toward the optimum is achieved by the crossover and mutation operations. GA is attractive since it uses only objective function values in the search process, so gradient calculations are avoided. Hence, GA are able to deal with discrete variables. Studies report success in the use of GA for aircraft design optimization studies, trajectory analysis, space structure design and control systems design. In these studies reliable convergence was achieved, but the number of function evaluations was large compared with efficient gradient methods. Applicaiton of GA is underway for a cost optimization study for a launch-vehicle fuel-tank and structural design of a wing. The strengths and limitations of GA for launch vehicle design optimization is studied.

Unal, Resit↗

Strategies for Automation of Model Tuning in Multifidelity Trajectory Uncertainty Propagation

Multi-model Monte Carlo methods are efficient strategies to perform forward uncertainty quantification studies in entry, descent, and landing (EDL) applications. These multi-model methods are based on the classical Monte Carlo estimator, but fuse predictions from several low-fidelity models to obtain estimators with greater precision given a prescribed computational budget. The effectiveness of these approaches relies on the magnitudes of correlations between the low-fidelity models and the high-fidelity model, as well as the relative computational costs of all models. Identifying and exploiting the best trade-off between correlation and cost, which ultimately depends on the selection of hyperparameters in the low-fidelity models, is a task often performed by hand or simply inspired by the deterministic understanding available for a specific application. This work extends a preliminary effort,

Marten Thompson↗

Near Earth Asteroid (NEA) Scout

NASA is developing solar sail propulsion for a near-term Near Earth Asteroid (NEA) reconnaissance mission that will lay the groundwork for the future use of solar sails. The NEA Scout mission will use the sail as primary propulsion allowing it to survey and image one NEA's of interest for future human exploration. NEA Scout will launch on the first mission of the Space Launch System (SLS) in 2018. After its first encounter with the Moon, NEA Scout will enter the sail characterization phase by the 86 square meter sail deployment. A mechanical Active Mass Translation (AMT) system, combined with the remaining ACS propellant, will be used for sail momentum management. The spacecraft will perform a series of lunar flybys to achieve optimum departure trajectory before beginning its two year-long cruise. About one month before the asteroid flyby, NEA Scout will start its approach phase using optical navigation on top of radio tracking. The solar sail will provide NEA Scout continuous low thrust to enable a relatively slow flyby of the target asteroid under lighting conditions favorable to geological imaging. Once complete, NASA will have demonstrated the capability to fly low-cost, high delta V CubeSats to perform interplanetary missions.

Johnson, Les↗

Digital detection and processing of laser beacon signals for aircraft collision hazard warning

A low-cost collision hazard warning system suitable for implementation in both general and commercial aviation is presented. Laser beacon systems are used as sources of accurate relative position information that are not dependent on communication between aircraft or with the ground. The beacon system consists of a rotating low-power laser beacon, detector arrays with special optics for wide angle acceptance and filtering of solar background light, microprocessors for proximity and relative trajectory computation, and pilot displays of potential hazards. The laser beacon system provides direct measurements of relative aircraft positions; using optimal nonlinear estimation theory, the measurements resulting from the current beacon sweep are combined with previous data to provide the best estimate of aircraft proximity, heading, minimium passing distance, and time to closest approach.

Sweet, L. M.↗

Project Morpheus: Lessons Learned in Lander Technology Development

NASA's Morpheus Project has developed and tested a prototype planetary lander capable of vertical takeoff and landing, that is designed to serve as a testbed for advanced spacecraft technologies. The lander vehicle, propelled by a LOX/Methane engine and sized to carry a 500kg payload to the lunar surface, provides a platform for bringing technologies from the laboratory into an integrated flight system at relatively low cost. Designed, developed, manufactured and operated in-house by engineers at Johnson Space Center, the initial flight test campaign began on-site at JSC less than one year after project start. After two years of testing, including two major upgrade periods, and recovery from a test crash that caused the loss of a vehicle, flight testing will evolve to executing autonomous flights simulating a 500m lunar approach trajectory, hazard avoidance maneuvers, and precision landing, incorporating the Autonomous Landing and Hazard Avoidance (ALHAT) sensor suite. These free-flights are conducted at a simulated planetary landscape built at Kennedy Space Center's Shuttle Landing Facility. The Morpheus Project represents a departure from recent NASA programs and projects that traditionally require longer development lifecycles and testing at remote, dedicated testing facilities. This paper expands on the project perspective that technologies offer promise, but capabilities offer solutions. It documents the integrated testing campaign, the infrastructure and testing facilities, and the technologies being evaluated in this testbed. The paper also describes the fast pace of the project, rapid prototyping, frequent testing, and lessons learned during this departure from the traditional engineering development process at NASA's Johnson Space Center.

Olansen, Jon B.↗

Wide-Field Infrared Survey Telescope and Starshade Formation Flying Dynamics at Sun-Earth L2

The formation flying of an occulter with a telescope at the Sun-Earth L2 (SEL2) Libration Point can be a challenging problem. A good knowledge of the Restricted Three Body Problem dynamics is required to understand how these two spacecraft interact with each other in the SEL2 unstable environment, and how other perturbations such as Solar Radiation Pressure (SRP) affect their mutual trajectories. This paper focuses on the transfer trajectories to achieve specific relative positions between two spacecraft as they fly in formation at SEL2, andanalyzes the relevance of SRP in this formation, using the Wide-Field Infrared Survey Telescope (WFIRST) and the Starshade occulter as an example. Given that WFIRST and Starshade have very different area-to-mass ratios, SRP will affect their motion in different ways, and their relative position can be key to reduce the V cost. In this paper we intend on providing an explanation on how the relative position between both spacecrafts affects the transfer V from one observation to the other using dynamical system theory and Floquet modes.

Pressure↗

New modelling capabilities in IDT

This work concerns the enhanced modelling capabilities of the discrete ordinates transport solver IDT. The novelties introduced allow for modelling unstructured geometries composed by a collection of X/Y segments and circles, and the use of reciprocity and conservation relations reduce the memory imprint as well as the computational cost of the method. IDT decomposes geometries in modular Cartesian patterns, which are the so-called Heterogeneous Cartesian Cells (HCCs), containing a chunk of the original unstructured geometries. Each HCC can be then discretized by superimposing a XY grid to refine locally the HCC. Unlike the most popular MOC, IDT performs the spatial sweeping by directional collision probabilities instead of trajectories. The sources and interface angular fluxes are expanded up to linear order. The accuracy of ray-tracing, the memory imprints together with the novel mesh refinement capabilities have been verified. A first set of preliminary results on PWR lattice problems will be presented in this paper.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Interplanetary program to optimize simulated trajectories (IPOST). Volume 4: Sample cases

The Interplanetary Program to Optimize Simulated Trajectories (IPOST) is intended to support many analysis phases, from early interplanetary feasibility studies through spacecraft development and operations. The IPOST output provides information for sizing and understanding mission impacts related to propulsion, guidance, communications, sensor/actuators, payload, and other dynamic and geometric environments. IPOST models three degree of freedom trajectory events, such as launch/ascent, orbital coast, propulsive maneuvering (impulsive and finite burn), gravity assist, and atmospheric entry. Trajectory propagation is performed using a choice of Cowell, Encke, Multiconic, Onestep, or Conic methods. The user identifies a desired sequence of trajectory events, and selects which parameters are independent (controls) and dependent (targets), as well as other constraints and the cost function. Targeting and optimization are performed using the Standard NPSOL algorithm. The IPOST structure allows sub-problems within a master optimization problem to aid in the general constrained parameter optimization solution. An alternate optimization method uses implicit simulation and collocation techniques.

Hong, P. E.↗