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

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At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Model-based and Model-free Designs for an Extended Continuous-time LQR with Exogenous Inputs

We present an extended linear quadratic regulator (LQR) design for continuous-time linear time-invariant (LTI) systems in the presence of exogenous inputs. We first propose a model-based solution with cost minimization guarantees for states and inputs using dynamic programming (DP). The control law consists of a combination of the optimal state feedback and an additional optimal term dependent on the exogenous inputs. The control gains for the two components are obtained by solving a set of matrix differential equations. We provide these solutions for both finite horizons and steady-state cases. In the second part of the paper, we formulate a reinforcement learning (RL) based algorithm which does not need any model information except the input matrix, and can compute an approximate steady-state LQR gain using measurements of the states, the control inputs, and the exogenous inputs. Both model-based and data-driven optimal control algorithms are tested with a numerical example under different exogenous inputs showcasing the effectiveness of the designs.

Mukherjee, Sayak↗
DOE OSTI2024

LoVoCCS. II. Weak Lensing Mass Distributions, Red-sequence Galaxy Distributions, and Their Alignment with the Brightest Cluster Galaxy in 58 Nearby X-Ray-luminous Galaxy Clusters

The Local Volume Complete Cluster Survey is an ongoing program to observe nearly a hundred low-redshift X-ray-luminous galaxy clusters (redshifts 0.03 < z < 0.12 and X-ray luminosities in the 0.1–2.4 keV band L X500c > 10 44 erg s −1 ) with the Dark Energy Camera, capturing data in the u, g, r, i, z bands with a 5σ point source depth of approximately 25th–26th AB magnitudes. Here, we map the aperture masses in 58 galaxy cluster fields using weak gravitational lensing. These clusters span a variety of dynamical states, from nearly relaxed to merging systems, and approximately half of them have not been subject to detailed weak lensing analysis before. In each cluster field, we analyze the alignment between the 2D mass distribution described by the aperture mass map, the 2D red-sequence (RS) galaxy distribution, and the brightest cluster galaxy (BCG). We find that the orientations of the BCG and the RS distribution are strongly aligned throughout the interiors of the clusters: the median misalignment angle is 19° within 2 Mpc. We also observe the alignment between the orientations of the RS distribution and the overall cluster mass distribution (by a median difference of 32° within 1 Mpc), although this is constrained by galaxy shape noise and the limitations of our cluster sample size. These types of alignment suggest long-term dynamical evolution within the clusters over cosmic timescales.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

FY21 Progress Report: SRNL Analysis of ICCWR LCM and WAMS data for Corrosion and Cracking

The development of algorithms for machine learning and data analysis for the 3013 Surveillance Program is a collaborative effort by the Savannah River National Laboratory (SRNL) and the University of South Carolina (USC). For corrosion detection, Laser Confocal Microscope (LCM) or Wide Area 3D Measurement System (WAMS) data is extracted from large binary files, with software written to convert the data to physical attributes (e.g., height, color and grayscale values; all as functions of a location in a plane projection). A user-friendly Matlab Graphical User Interface (GUI) that reads data from either LCM or WAMS files was developed to integrate input data with software developed for processing and evaluation. The GUI can selectively download binary data, interrogate data attributes, label data, flag significant features, execute Machine Learning (ML) algorithms, output parameters for trained ML algorithms, report ML model accuracy with respect to labeled data, and generate graphical representations for various analyses. Features can be called out by user-specified thresholds, manual labeling or machine learning algorithms when they have been completed. The ability to rapidly label data is important because of the volume of data required for training machine learning algorithms. The GUI has the flexibility to allow addition of improved ML algorithms, methods for data visualization, and statistical computations. Statistical analyses via the GUI include areas of pits within a defined range of pit depths, correlations between Red-Green-Blue (RGB) or grayscale intensity and relative surface height, covariances between values associated with features, and feature histograms. The development of supervised machine learning algorithms, however, has been hindered by a lack of training data. The machine learning algorithms for crack identification are being refined but require improvements to the true positive rate for crack detection. This shortcoming is an artifact of the limited training data currently available, perhaps more so than the structure of the neural networks. At present, the best results are had from a consensus over an ensemble of randomly generated Deep Neural Network (DNN) or Convolutional Neural Network (CNN) algorithms. Although the consensus accuracy method has yielded optimum true positive and true negative rates in excess of 80%, additional validation testing is necessary. In addition to the suite of LCM data that was initially used, and which represents the majority of the work presented in this report, WAMS image data was also reviewed at a preliminary level. The review included a comparison between image resolution and dynamic range for each method. WAMS (ZON file) image data was found to have a pixel pitch of 3.69μm compared to 1 μm for the LCM (vk4 file) data, which implies a lower resolution for the WAMS images. Conversely, the ratio of dynamic range of the WAMS data to the LCM data was approximately 41:20 for height data, suggesting that information from WAMS should more accurately determine the depth of pits. At present, the significance of the greater dynamic range of the WAMS data relative to the LCM data has not yet been evaluated.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2024

ELECTRONIC STRUCTURE METHODS AND PROTOCOLS WITH APPLICATION TO DYNAMICS, KINETICS AND THERMOCHEMISTRY

Hydrocarbon combustion involves the reaction dynamics of a tremendous number of species beginning with many-component fuel mixtures and proceeding via a complex system of intermediates to form primary and secondary products. Combustion conditions corresponding to new advanced engines and/or alternative fuels rely increasingly on autoignition and low-temperature-combustion chemistry. In these regimes various transient radical species such as HO2, ROO·, ·QOOH, HCO, NO2, HOCO, and Criegee intermediates play important roles in determining the detailed as well as more general dynamics. A clear understanding and accurate representation of these processes is needed for effective modeling. Given the difficulties associated with making reliable experimental measurements of these systems, computation can play an important role in developing these energy technologies. Accurate calculations have their own challenges since even within the simplest dynamical approximations such as transition state theory, the rates depend exponentially on critical barrier heights and these may be sensitive to the level of quantum chemistry. Moreover, it is well-known that in many cases it is necessary to go beyond statistical theories and consider the dynamics. Quantum tunneling, resonances, radiative transitions, and non-adiabatic effects governed by spin-orbit or derivative coupling can be determining factors in those dynamics. Building upon progress made during a period of prior support through the DOE Early Career Program, this project combines developments in the areas of potential energy surface (PES) fitting and multistate multireference quantum chemistry to allow spectroscopically and dynamically/kinetically accurate investigations of key molecular systems (such as those mentioned above), many of which are radicals with strong multireference character and have the possibility of multiple electronic states contributing to the observed dynamics. An ongoing area of investigation is to develop general strategies for robustly convergent electronic structure theory for global multichannel reactive surfaces including diabatization of energy and other relevant surfaces such as dipole transition. Combining advances in ab initio methods with automated interpolative PES fitting allows the construction of high-quality PESs (incorporating thousands of high-level data) to be done rapidly through parallel processing on high-performance computing (HPC) clusters. In addition, new methods and approaches to electronic structure theory will be developed and tested through applications. This project will explore limitations in traditional multireference calculations (e.g., MRCI) such as those imposed by internal contraction, lack of high-order correlation treatment and poor scaling. Methods such as DMRG-based extended active-space CASSCF and various Quantum Monte Carlo (QMC) methods will be applied (including VMC/DMC and FCIQMC). Insight into the relative significance of different orbital spaces and the robustness of application of these approaches on leadership class computing architectures will be gained. Synergy with other components of this research program such as automated PES fitting and multireference quantum chemistry will be used to address challenges encountered by the standard approaches to computational thermochemistry (those being single-reference quantum chemistry and perturbative treatments of the anharmonic vibrational energy, which break down for some cases of electronic structure or floppy strongly coupled vibrational modes).

74 ATOMIC AND MOLECULAR PHYSICS↗
NASA NTRS1983

A program of research in environmental modeling

A theoretical framework for the interpretation of satellite measurements of stratospheric temperature and trace gases is provided. This problem is quite complicated since the distributions of trace gases are dependent on dynamics and photochemistry. Therefore, the problem was attacked with models employing varying degrees of photochemical and dynamical complexity. The relationship between dynamics and trace gas transport and wave transience, dissipation and critical levels and the net (permanent) transport of trace gases, the role of photochemistry in trace gas transport, photochemistry and dynamics and altering the mean-zonal distribution of stratospheric ozone, and approximations to simplify the interpretation of observations and General Circulation Models are discussed.

Source record↗
NASA NTRS1982

A Piecewise Linear State Variable Technique for Real Time Propulsion System Simulation

The emphasis on increased aircraft and propulsion control system integration and piloted simulation has created a need for higher fidelity real time dynamic propulsion models. A real time propulsion system modeling technique which satisfies this need and which provides the capabilities needed to evaluate propulsion system performance and aircraft system interaction on manned flight simulators was developed and demonstrated using flight simulator facilities at NASA Ames. A piecewise linear state variable technique is used. This technique provides the system accuracy, stability and transient response required for integrated aircraft and propulsion control system studies. The real time dynamic model includes the detail and flexibility required for the evaluation of critical control parameters and propulsion component limits over a limited flight envelope. The model contains approximately 7.0 K bytes of in-line computational code and 14.7 K of block data. It has an 8.9 ms cycle time on a Xerox Sigma 9 computer. A Pegasus-Harrier propulsion system was used as a baseline for developing the mathematical modeling and simulation technique. A hydromechanical and water injection control system was also simulated. The model was programmed for interfacing with a Harrier aircraft simulation at NASA Ames. Descriptions of the real time methodology and model capabilities are presented.

Mihaloew, J. R.↗
NASA NTRS1982

A piecewise linear state variable technique for real time propulsion system simulation

The emphasis on increased aircraft and propulsion control system integration and piloted simulation has created a need for higher fidelity real time dynamic propulsion models. A real time propulsion system modeling technique which satisfies this need and which provides the capabilities needed to evaluate propulsion system performance and aircraft system interaction on manned flight simulators was developed and demonstrated using flight simulator facilities at NASA Ames. A piecewise linear state variable technique is used. This technique provides the system accuracy, stability and transient response required for integrated aircraft and propulsion control system studies. The real time dynamic model includes the detail and flexibility required for the evaluation of critical control parameters and propulsion component limits over a limited flight envelope. The model contains approximately 7.0 K bytes of in-line computational code and 14.7 K of block data. It has an 8.9 ms cycle time on a Xerox Sigma 9 computer. A Pegasus-Harrier propulsion system was used as a baseline for developing the mathematical modeling and simulation technique. A hydromechanical and water injection control system was also simulated. The model was programmed for interfacing with a Harrier aircraft simulation at NASA Ames. Descriptions of the real time methodology and model capabilities are presented.

Mihaloew, J. R.↗
NASA NTRS1989

Steady and unsteady transonic small disturbance analysis of realistic aircraft configurations

A transonic unsteady aerodynamic and aeroelastic code called CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) was developed for application to realistic aircraft configurations. It permits the calculation of steady and unsteady flows about complete aircraft configurations for aeroelastic analysis of the flutter critical transonic speed range. The CAP-TSD code uses a time accurate approximate factorization algorithm for solution of the unsteady transonic small disturbance potential equation. An overview is given of the CAP-TSD code development effort along with recent algorithm modifications which are listed and discussed. Calculations are presented for several configurations including the General Dynamics 1/9th scale F-16C aircraft model to evaluate the algorithm and hence the reliability of the CAP-TSD code in general. Calculations are also presented for a flutter analysis of a 45 deg sweptback wing which agree well with the experimental data. Descriptions are presented of the CAP-TSD code and algorithm details along with results and comparisons which demonstrate the stability, accuracy, efficiency, and utility of CAP-TSD.

Batina, John T.↗
NASA NTRS1988

Review and assessment of the HOST turbine heat transfer program

The objectives of the HOST Turbine Heat Transfer subproject were to obtain a better understanding of the physics of the aerothermodynamic phenomena occurring in high-performance gas turbine engines and to assess and improve the analytical methods used to predict the fluid dynamics and heat transfer phenomena. At the time the HOST project was initiated, an across-the-board improvement in turbine design technology was needed. Therefore, a building-block approach was utilized, with research ranging from the study of fundamental phenomena and analytical modeling to experiments in simulated real-engine environments. Experimental research accounted for 75 percent of the project, and analytical efforts accounted for approximately 25 percent. Extensive experimental datasets were created depicting the three-dimensional flow field, high free-stream turbulence, boundary-layer transition, blade tip region heat transfer, film cooling effects in a simulated engine environment, rough-wall cooling enhancement in a rotating passage, and rotor-stator interaction effects. In addition, analytical modeling of these phenomena was initiated using boundary-layer assumptions as well as Navier-Stokes solutions.

Gladden, Herbert J.↗
NASA NTRS1989

Stability and dynamic analysis of a slender column with curved longitudinal stiffeners

The results of a stability design study are presented for a slender column with curved longitudinal stiffeners for large space structure applications. Linear stability analyses are performed using a link-plate representation of the stiffeners to determine stiffener local buckling stresses. Results from a set of parametric analyses are used to determine an approximate explicit expression for stiffener local buckling in terms of its geometric parameters. This expression along with other equations governing column stability and mass are assembled into a determinate system describing minimum mass stiffened column design. An iterative solution is determined to solve this system and a computer program incorporating this routine is presented. Example design problems are presented which verify the solution accuracy and illustrate the implementation of the solution routine. Also, observations are made which lead to a greatly simplified first iteration design equation relating the percent increase in column mass to the percent increase in column buckling load. From this, generalizations are drawn as to the mass savings offered by the stiffened column concept. Finally, the percent increase in fundamental column vibration frequency due to the addition of deployable stiffeners is studied.

Lake, Mark S.↗
NASA NTRS2015

Monitoring Changes of Tropical Extreme Rainfall Events Using Differential Absorption Barometric Radar (DiBAR)

This work studies the potential of monitoring changes in tropical extreme rainfall events such as tropical storms from space using a Differential-absorption BArometric Radar (DiBAR) operating at 50-55 gigahertz O2 absorption band to remotely measure sea surface air pressure. Air pressure is among the most important variables that affect atmospheric dynamics, and currently can only be measured by limited in-situ observations over oceans. Analyses show that with the proposed radar the errors in instantaneous (averaged) pressure estimates can be as low as approximately 5 millibars (approximately 1 millibar) under all weather conditions. With these sea level pressure measurements, the forecasts, analyses and understanding of these extreme events in both short and long time scales can be improved. Severe weathers, especially hurricanes, are listed as one of core areas that need improved observations and predictions in WCRP (World Climate Research Program) and NASA Decadal Survey (DS) and have major impacts on public safety and national security through disaster mitigation. Since the development of the DiBAR concept about a decade ago, our team has made substantial progress in advancing the concept. Our feasibility assessment clearly shows the potential of sea surface barometry using existing radar technologies. We have developed a DiBAR system design, fabricated a Prototype-DiBAR (P-DiBAR) for proof-of-concept, conducted lab, ground and airborne P-DiBAR tests. The flight test results are consistent with our instrumentation goals. Observational system simulation experiments for space DiBAR performance show substantial improvements in tropical storm predictions, not only for the hurricane track and position but also for the hurricane intensity. DiBAR measurements will lead us to an unprecedented level of the prediction and knowledge on tropical extreme rainfall weather and climate conditions.

Lin, Bing↗
DOE OSTI2021

Simulating non-native cubic interactions on noisy quantum machines

As a milestone for general-purpose computing machines, we demonstrate that quantum processors can be programed to efficiently simulate dynamics that are not native to the hardware. Moreover, on noisy devices without error correction, we show that simulation results are significantly improved when the quantum program is compiled using modular gates instead of a restricted set of standard gates. We demonstrate the general methodology by solving a cubic interaction problem, which appears in nonlinear optics, gauge theories, as well as plasma and fluid dynamics. To encode the non-native Hamiltonian evolution, we decompose the Hilbert space into a direct sum of invariant subspaces in which the nonlinear problem is mapped to a finite-dimensional Hamiltonian simulation problem. Furthermore, in a three-states example, the resultant unitary evolution is realized by a product of approximately 20 standard gates, using which approximately ten simulation steps can be carried out on state-of-the-art quantum hardware before results are corrupted by decoherence. In comparison, the simulation depth is improved by more than an order of magnitude when the unitary evolution is realized as a single cubic gate, which is compiled directly using optimal control. Alternatively, parametric gates may also be compiled by interpolating control pulses. Modular gates thus obtained provide high-fidelity building blocks for quantum Hamiltonian simulations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2011

Flight Test Results from the Rake Airflow Gage Experiment on the F-15B

The results are described of the Rake Airflow Gage Experiment (RAGE), which was designed and fabricated to support the flight test of a new supersonic inlet design using Dryden's Propulsion Flight Test Fixture (PFTF) and F-15B testbed airplane (see figure). The PFTF is a unique pylon that was developed for flight-testing propulsion-related experiments such as inlets, nozzles, and combustors over a range of subsonic and supersonic flight conditions. The objective of the RAGE program was to quantify the local flowfield at the aerodynamic interface plane of the Channeled Centerbody Inlet Experiment (CCIE). The CCIE is a fixed representation of a conceptual mixed-compression supersonic inlet with a translating biconic centerbody. The primary goal of RAGE was to identify the relationship between free-stream and local Mach number in the low supersonic regime, with emphasis on the identification of the particular free-stream Mach number that produced a local Mach number of 1.5. Measurements of the local flow angularity, total pressure distortion, and dynamic pressure over the interface plane were also desired. The experimental data for the RAGE program were obtained during two separate research flights. During both flights, local flowfield data were obtained during straight and level acceleration segments out to steady-state test points. The data obtained from the two flights showed small variations in Mach number, flow angularity, and dynamic pressure across the interface plane at all flight conditions. The data show that a free-stream Mach number of 1.65 will produce the desired local Mach number of 1.5 for CCIE. The local total pressure distortion over the interface plane at this condition was approximately 1.5%. At this condition, there was an average of nearly 2 of downwash over the interface plane. This small amount of downwash is not expected to adversely affect the performance of the CCIE inlet.

Frederick, Michael↗
NASA NTRS1986

The LATDYN user's manual

The LATDYN User's Manual presents the capabilities and instructions for the LATDYN (Large Angle Transient DYNamics) computer program. The LATDYN program is a tool for analyzing the controlled or uncontrolled dynamic transient behavior of interconnected deformable multi-body systems which can undergo large angular motions of each body relative other bodies. The program accommodates large structural deformation as well as large rigid body rotations and is applicable, but not limited to, the following areas: (1) development of large flexible space structures; (2) slewing of large space structure components; (3) mechanisms with rigid or elastic components; and (4) robotic manipulations of beam members. Presently the program is limited to two dimensional problems, but in many cases, three dimensional problems can be exactly or approximately reduced to two dimensions. The program uses convected finite elements to affect the large angular motions involved in the analysis. General geometry is permitted. Detailed user input and output specifications are provided and discussed with example runstreams. To date, LATDYN has been configured for CDC/NOS and DEC VAX/VMS machines. All coding is in ANSII-77 FORTRAN. Detailed instructions regarding interfaces with particular computer operating systems and file structures are provided.

Housner, J. M.↗
NASA NTRSDate not supplied

Multiphase Simulations of the SLS Launch Environment

NASA’s Space Launch System (SLS), which will send astronauts back to the Moon in the next few years, is powered by four RS-25 engines and two RSRMV solid rocket boosters (SRBs). During launch the SLS propulsion system generates intense acoustics and other powerful waves, such as ignition overpressure (IOP) which, if unmitigated, have the potential to damage the vehicle and possibly cause loss of mission or crew. To protect the vehicle from these powerful waves, the SLS launch pad design includes an ignition overpressure/sound suppression (IOP/SS) system which sprays 270,000 gallons per minute of water very close to the SRB and RS-25 nozzles. The SRB and RS-25 engine plumes, and the proximity of the IOP/SS water, create a complex multiphase (gas and liquid) environment during the SLS ignition sequence. The interplay among these systems creates challenges related to water spray into/onto engine nozzles, potential debris transport, and additional transient loads due to strong plume-water interactions - all of which the SLS vehicle must be able to withstand. Prior to the Artemis I launch, the SLS multiphase liftoff environment was largely unknown due to differences from the Space Shuttle and other programs. Some data was available from tests of individual systems, but no integrated testing or analysis was available. Even post-launch analysis of Artemis I cannot provide a full understanding of the complex physics involved due to limited (or obstructed) camera views and instrumentation. Computational fluid dynamics (CFD) is being used to investigate the details of the multiphase environment which could not be measured, help comprehend the data gathered from the launch, and ultimately identify phenomena that are a concern for future flights. Project Details Engineers at NASA’s Marshall Space Flight Center (MSFC) have executed simulations using the Loci/STREAM-Volume of Fluid (VoF) multiphase CFD solver to understand this environment. Initial efforts successfully validated the CFD solver on various tests, giving confidence to simulate the SLS multiphase liftoff environment prior to the Artemis I launch. The CFD simulation of the SLS ignition sequence was conducted in three phases. First the IOP/SS water system was simulated for approximately 6 seconds to reach a quasi-steady state. Next, the RS-25 engine plumes were activated and held at full power for 1 second. Lastly, the SRB booster was activated and the simulation was carried out until just prior to vehicle motion. This simulation process mimics the conditions that exist at launch. Results and Impact The SLS ignition sequence simulation results provide deep understanding of the underlying physics occuring during launch. Observations from the simulation include reduction of water splashing into/onto the engine nozzles, change in angling of the dense water sheets, and the origin of the powerful ignition overpressure (IOP) wave. These observations directly inform the SLS program on subjects including plume-water induced side loads, debris transport, and the acoustic launch environment. Additionally, with post launch comparison of CFD observations to flight data, these tools can be applied to launch vehicles and environments other than SLS with confidence. Why HPC Matters The SLS ignition sequence CFD simulations are conducted on meshes up to hundreds of millions of cells on thousands of processors for weeks at a time. These simulations generate terabytes of data that must also be stored and archived for future use on HPC systems. Simply put, the CFD simulations would not be possible without NASA HPC resources. What’s Next Comparisons between the Artemis I flight data and the CFD simulations will be continued to both improve confidence in the CFD results and provide deeper understanding into the SLS multiphase launch environment. This will be used to provide insight for decision making for the first manned SLS flight, Artemis II. Future simulations will target new configurations of the SLS IOP/SS water required to support the more powerful variants of the SLS vehicle, such as Block 1B. Additionally, this capability provides NASA the ability to investigate launch environments for vehicles other than SLS to support other missions.

Travis Rivord↗
NASA NTRS1975

Three-dimensional dynamics of scientific balloon systems in response to sudden gust loadings

A mathematical model was developed of the three-dimensional dynamics of a high-altitude scientific research balloon system perturbed from its equilibrium configuration by an arbitrary gust loading. The platform is modelled as a system of four coupled pendula, and the equations of motion were developed in the Lagrangian formalism assuming a small-angle approximation. Three-dimensional pendulation, torsion, and precessional motion due to Coriolis forces are considered. Aerodynamic and viscous damping effects on the pendulatory and torsional motions are included. A general model of the gust field incident upon the balloon system was developed. The digital computer simulation program is described, and a guide to its use is given.

Dorsey, D. R., Jr.↗
NASA NTRS1972

Considerations for an earth physics information-management service.

In a preliminary investigation into the feasibility of establishing a data center for earth physics, 12 disciplines were considered for inclusion. Estimation of the size of the data base for each indicated a need for storage of approximately 10 to the 10th power characters. The computer-based system deemed most worthy of further investigation was the interactive concept with remote-terminal access. Users are divided into three classes according to how they would access information: with no terminal, with an interactive terminal, and with a multidevice terminal. All these users can be served by the same center without any particular difficulty, but the real benefactor is the user with an interactive terminal, because he can compile, debug, and run programs in one continuous session. Final points stressed are multiprogramming for dynamic resource sharing, hardware modularity for future expansion, and information protection for such a large community of users. It is concluded that a survey should be conducted to gather more information from the potential users of such a system, and that a pilot project should be developed at some location where both earth-physics research and data-processing capabilities already exist.

Martin, R. W.↗
NASA NTRS1978

Minimum energy control of a class of electrically driven vehicles

Theoretical and experimental results are obtained in the investigation of a minimum energy control problem associated with a class of electrically driven vehicles. Analytical results are obtained by making several justifiable approximations in the dynamical equations of the plant, the performance index of which is related to the minimization of system energy consumption for any required control action. The control problem of interest is simplified and solved by using Bellman's invariant imbedding technique. The optimality of the resulting control law is compared with those of the bang-bang control law, which is the exact solution for the case of speed-setting control action, and the classical control laws under identical conditions. A stochastic optimization problem is then formulated and solved by using Bellman's dynamic programming technique. The resulting control law is mechanized for a particular vehicle configuration which is simulated in the laboratory.

Sahinkaya, Y. E.↗