Search NASA⌕ Search

SEARCH · Search NASA

Results for “process optimization and control”

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 487 records · Page 27
All sourcesNASA NTRSDOE OSTI
NASA NTRSDate not supplied

Multi-Impulse to Time Optimal Finite Burn Trajectory Conversion

A novel algorithm is presented that provides an improvement over a traditional parameter optimization method when solving time-optimal, finite-burn pseudo-rendezvous spacecraft trajectory problems. A hybrid optimization procedure is described that converts a set of multiple-impulses, representing high- or low-thrust maneuvers, to an exact time-optimal finite-burn trajectory for a thrust limited, constant exhaust velocity spacecraft. The Hybrid Method applies a control law derived from the Euler-Lagrange system of equations within the classical Indirect Method to a modern Direct Method. An iterative adjoint-control transformation and an evolving constraint vector are introduced to solve the optimal control two-point boundary value problem. This method requires no prior knowledge of the solution, which adds simplicity to the trajectory design process and aids automation. Examples are shown for low-thrust apogee raise maneuvers, non-coplanar Earth orbit transfers, and a modified Deep Space 1 low-thrust trajectory. A numerically significant improvement to objective cost is shown across all application problems compared to a traditional solution method, as well as a significant improvement to convergence speed for a select class of problems.

Joshua A Fogel↗
DOE OSTI2025

Unveiling the Role of In Situ Al 2 O 3 Passivation in Molecular-Ink-Processed CuIn(S,Se) 2 Photovoltaics

Here, we report on the optimization of in situ passivation of ink-based CuIn(S,Se) 2 thin-film solar cells via controlled incorporation of Al 2 O 3 in CuIn(S,Se) 2 films by the addition of Al(NO 3 ) 3 to the molecular ink precursor. For this purpose, the Al/(Al + In) (AAI) metal ratio was varied from 0.05 to 0.30. We observe that the efficiency of the cells made of Al 2 O 3 -incorporated CuIn(S,Se) 2 is consistently higher than those without Al 2 O 3 , especially due to an improvement in open-circuit voltage (V OC ) and fill factor (FF), for all tested AAI ratios. With an AAI of 0.05, a maximum efficiency of 11.2% and an average efficiency of 8.5% (measured across 18 cells) was achieved, compared to 8.5% maximum efficiency and 6.5% average efficiency for Al-free CuIn(S,Se) 2 . Furthermore, we find that cells made of Al 2 O 3 -incorporated CuIn(S,Se) 2 with an AAI of 0.2 show a narrow distribution in the photovoltaic performance, indicating higher reproducibility and higher FF. Energy-dispersive X-ray spectroscopy shows that, at AAI = 0.2, Al 2 O 3 is distributed more homogeneously at the surface of the Al 2 O 3 -incorporated CISSe. Capacitance-voltage measurements reveal a reduced defect density by incorporation of Al 2 O 3 , which could be partly responsible for the higher V OC . Furthermore, using detailed surface analysis with various X-ray and electron spectroscopy methods, we derive chemical and electronic structure information from the surface. With ultraviolet photoelectron (UPS) and inverse photoemission spectroscopies (IPES), the electronic band gap of the CuIn(S,Se) 2 thin-film surface is found to increase from 1.22 to 1.88 eV (+-0.12 eV) with Al 2 O 3 incorporation. This is accompanied by a clear reduction of the conduction band spike at the CdS/CISSe interface due to Al 2 O 3 addition, as derived by both UPS and IPES as well as temperature-dependent V OC measurements.

14 SOLAR ENERGY↗
NASA NTRS1992

Intelligent sensor-model automated control of PMR-15 autoclave processing

An intelligent sensor model system has been built and used for automated control of the PMR-15 cure process in the autoclave. The system uses frequency-dependent FM sensing (FDEMS), the Loos processing model, and the Air Force QPAL intelligent software shell. The Loos model is used to predict and optimize the cure process including the time-temperature dependence of the extent of reaction, flow, and part consolidation. The FDEMS sensing system in turn monitors, in situ, the removal of solvent, changes in the viscosity, reaction advancement and cure completion in the mold continuously throughout the processing cycle. The sensor information is compared with the optimum processing conditions from the model. The QPAL composite cure control system allows comparison of the sensor monitoring with the model predictions to be broken down into a series of discrete steps and provides a language for making decisions on what to do next regarding time-temperature and pressure.

Hart, S.↗
NASA NTRS1997

Constrained Multipoint Aerodynamic Shape Optimization Using an Adjoint Formulation and Parallel Computers

An aerodynamic shape optimization method that treats the design of complex aircraft configurations subject to high fidelity computational fluid dynamics (CFD), geometric constraints and multiple design points is described. The design process will be greatly accelerated through the use of both control theory and distributed memory computer architectures. Control theory is employed to derive the adjoint differential equations whose solution allows for the evaluation of design gradient information at a fraction of the computational cost required by previous design methods. The resulting problem is implemented on parallel distributed memory architectures using a domain decomposition approach, an optimized communication schedule, and the MPI (Message Passing Interface) standard for portability and efficiency. The final result achieves very rapid aerodynamic design based on a higher order CFD method. In order to facilitate the integration of these high fidelity CFD approaches into future multi-disciplinary optimization (NW) applications, new methods must be developed which are capable of simultaneously addressing complex geometries, multiple objective functions, and geometric design constraints. In our earlier studies, we coupled the adjoint based design formulations with unconstrained optimization algorithms and showed that the approach was effective for the aerodynamic design of airfoils, wings, wing-bodies, and complex aircraft configurations. In many of the results presented in these earlier works, geometric constraints were satisfied either by a projection into feasible space or by posing the design space parameterization such that it automatically satisfied constraints. Furthermore, with the exception of reference 9 where the second author initially explored the use of multipoint design in conjunction with adjoint formulations, our earlier works have focused on single point design efforts. Here we demonstrate that the same methodology may be extended to treat complete configuration designs subject to multiple design points and geometric constraints. Examples are presented for both transonic and supersonic configurations ranging from wing alone designs to complex configuration designs involving wing, fuselage, nacelles and pylons.

Reuther, James↗
NASA NTRS2007

Optimisation of the Future Routine Orbit for Mars Express

Mars Express (MEX), the first planetary mission of the European Space Agency (ESA), reached Mars on December 25th 2003. Since then it is performing routine operations. Its operational phase had to cover one Martian year, with the possibility of an extension for a second Martian year (i.e. until November 2007). The end of the mission extension is approaching but, given the good health of the payload instruments and the high science return of the mission, there is a strong will to achieve further extensions. Mars Express is also seen as an important asset, capable to provide relay functions for future Martian missions. The ESA Science Program Committee has recently approved a second extension of the MEX mission until May 2009 and even further extensions are possible. Mars Express has an eccentric quasi-polar orbit with a period of approximately 6.72 hours and a pericentre height of about 300 km. Science observations are mainly performed at pericentre (but not only). In addition the orbit has a resonance of 11 revolutions per 3 Martian days. This means that ground tracks corresponding to orbits separated by 11 revolutions are adjacent, such that a given area can be covered by the on-board camera without leaving gaps. The J2 effect of Mars causes a drift of both ascending node and argument of pericentre. The drift of argument of pericentre makes it possible to observe periodically all Mars latitudes from close distance. Illumination conditions at pericentre are influenced by both the drift of the argument of pericentre and the drift of ascending node, as well as by the rotation of Mars around the Sun. The original MEX routine orbit was optimized for the duration of the nominal mission and extension, such that it produced a balanced share of day-side observations (for the optical instruments) and night-side observations (for the radar). The orbit was thus not optimized for the time beyond the assumed extension. Indeed, the evolution of the ascending node and argument of pericentre would cause in the following years a drift of the pericentre towards night-side observation conditions, hence uninteresting for the optical instruments. In order to prevent this an optimisation process for the future routine orbit has taken place. The share between day-side and night-side observations can be controlled by adjusting the drift of argument of pericentre and ascending node. This can in particular be achieved by changing the semimajor axis, eccentricity and/or inclination. A change of inclination is inefficient compared to a change in semimajor axis and eccentricity, and has therefore been discarded. An in-plane maneuvre can be performed to change both semi-major axis and eccentricity, and thus the period of the orbit. Although an apocentre manoeuvre is cheaper in terms of deltaV, it would result in raising the pericentre height, which is unfavourable for close observations. Hence a pericentre manoeuvre is proposed, which will increase the apocentre height. A repeat cycle is still required to allow mapping areas with adjacent ground tracks, so the change of semimajor axis must result in a new resonance. Resonances 18:5, 25:7 and 7:2 have been considered as potential candidates. The resulting long term evolution of the observation conditions has been analysed. Finally it has been decided to perform a change of orbit to reach the 18:5. Another aspect of the optimisation process is the control of the ground track. The previous MEX reference trajectory included regular maneuvres at every apocentre in order to adjust the orbital period, such that the separation of the ground tracks would be optimal, regardless of the latitude of pericentre. The implementation of the actual delatVs on-board was done partly by optimizing the attitude of reaction-wheel desaturation activities. Despite of it, this strategy has a significant propellant cost, because it prevents to optimize reaction wheel de-saturation activities to minimize propellant consumption. Therore, with the aim at preserving propellant resources for a long time extension it has been agreed to stop the ground-track control. This requires now a more accurate science operation planning, with improved attitude pointing control. Finally, the approach to phase Mars Express to provide back-up relay functions for NASA Phoenix landing is explained. In the context of the routine trajectory optimisation a new requirement for close fly-bys at Phobos, with different observation geometries, has been specified. The approach to fulfill this requirement is explained.

Carranza, Manuel↗
DOE OSTI2026

Scale-Up of Electrode Coating and Flow-Field for Commercial Hydrogen Peroxide Electrolyzer: Cooperative Research and Development Final Report, CRADA Number CRD-17-00687

Hydrogen peroxide is currently produced at central chemical plants via the anthraquinone oxidation process. This process produces environmental pollutants that are costly to remediate, requires hazardous long distance shipping of highly concentrated peroxide (50% or 70%), and necessitates extra handling costs related to storage and dilution. Peroxygen Systems, Inc. (PSi) is developing breakthrough technology for on-site hydrogen peroxide production. PSi’s on-site on-demand electrolyzer can reduce the cost of producing hydrogen peroxide by 50%, while also completely eliminating the cost and safety issues associated with shipping and handling of high concentration hydrogen peroxide. The challenge for PSi is scaling. To support the next step toward commercialization (customer pilot tests), scaling the prototype into larger single cells and 20-40 cell stacks is required. In addition to internal hardware and flow-field design efforts at PSi, NREL will address three critical problems for this scale-up effort: (1) demonstrating a large scale roll-to-roll (R2R) process to coat uniform electrode materials for 100 cm2 and 500 cm2 stack testing, (2) demonstrating an in-line diagnostic to achieve better electrode quality control, and (3) performing in situ cell/stack testing to better understand and optimize the performance of the flow field design.

28 EE - Advanced Manufacturing Office (EE-5A)↗
DOE OSTI2025

Post-build stress-relief optimization for laser powder bed fusion 316H stainless steel

Nuclear energy remains a critical component of a diversified and efficient energy portfolio, offering reliable, high-capacity, and low-carbon power. However, in the U.S., aging infrastructure and the slow qualification and deployment of advanced materials and manufacturing techniques hinder progress in next-generation reactor technologies. This study explores the application of laser powder bed fusion (LPBF) additive manufacturing for stainless steel 316H, with a focus on optimizing post-build heat treatments to enhance material properties for high-temperature nuclear applications. The research targets the optimization of stress-relief temperatures to alleviate postbuild residual stresses, ensuring improvements in the microstructural corelated properties. A series of microstructural and mechanical evaluations were performed on LPBF-printed SS-316H samples which were subjected to annealing at temperatures varying between 650 °C and 850 °C. X-ray diffraction, scanning electron microscopy, and transmission electron microscopy analyses revealed that increasing the heattreatment temperature accelerated dislocation recovery. Vickers microhardness measurements showed an initial reduction in values, followed by stabilization over extended durations at all the temperatures. While higher temperatures facilitated faster recovery, they also promoted carbide precipitation along grain and solidification cell boundaries, narrowing the safe processing window. In contrast, heat treatment at 650°C preserved the cellular substructure and enabled controlled carbide precipitation over time. In conclusion, these findings highlight the importance of time–temperature optimization and suggest that 650°C for up to 2 h provides the most favorable balance between recovery and carbide control for a stress-relief treatment.

316 stainless steel↗
DOE OSTI2025

Application of Advanced Materials Processing to Enable Direct Production of Fast Reactor Fuel Alloys

Argonne National Laboratory (the Contractor), located in Lemont, IL, and Oklo, Inc. (the Participant), headquartered in Sunnyvale, CA, entered into a Cooperative Research and Development Agreement (CRADA) to integrate advanced electrorefining co-deposition and molten-salt monitoring technologies to produce a uranium-transuranic (U/TRU) alloy within a controlled composition range that can be used as fast reactor fuel for Oklo, Inc.’s advanced reactor technology. Argonne performed the integration of electrorefining and process monitoring technologies, determined operating parameters for producing U/TRU alloys, and developed optimized design and operating parameters for co-deposition of U/TRU alloys. Oklo, Inc. worked with Argonne and the Nuclear Regulatory Commission (NRC) to provide the necessary process documentation to begin implementing pyroprocessing technology in the fast reactor fuel production process. Outcomes of this project included a pilot-scale co-deposition cathode design and technical basis for the operation of the co-deposition electrorefiner to produce U/TRU alloys with controlled composition.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

Leveraging prior mean models for faster Bayesian optimization of particle accelerators

Tuning particle accelerators is a challenging and time-consuming task that can be automated and carried out efficiently using suitable optimization algorithms, such as model-based Bayesian optimization techniques. One of the major advantages of Bayesian algorithms is the ability to incorporate prior information about beam physics and historical behavior into the model used to make control decisions. In this work, we examine incorporating prior accelerator physics information into Bayesian optimization algorithms by utilizing fast executing, neural network models trained on simulated or historical datasets as prior mean functions in Gaussian process models. We show that in ideal cases, this technique substantially increases convergence speed to optimal solutions in high-dimensional tuning parameter spaces. Additionally, we demonstrate that even in non-ideal cases, where prior models of beam dynamics do not exactly match experimental conditions, the use of this technique can still enhance convergence speed. Finally, we demonstrate how these methods can be used to improve optimization in practical applications, such as transferring information gained from beam dynamics simulations to online control of the LCLS injector, and transferring knowledge gained from experimental measurements across different operating modes, such as accelerating different ion species at the ATLAS heavy ion accelerator.

43 PARTICLE ACCELERATORS↗
DOE OSTI2024

SARS-CoV-2 wastewater variant surveillance: pandemic response leveraging FDA’s GenomeTrakr network

ABSTRACT Wastewater surveillance has emerged as a crucial public health tool for population-level pathogen surveillance. Supported by funding from the American Rescue Plan Act of 2021, the FDA‘s genomic epidemiology program, GenomeTrakr, was leveraged to sequence SARS-CoV-2 from wastewater sites across the United States. This initiative required the evaluation, optimization, development, and publication of new methods and analytical tools spanning sample collection through variant analyses. Version-controlled protocols for each step of the process were developed and published on protocols.io. A custom data analysis tool and a publicly accessible dashboard were built to facilitate real-time visualization of the collected data, focusing on the relative abundance of SARS-CoV-2 variants and sub-lineages across different samples and sites throughout the project. From September 2021 through June 2023, a total of 3,389 wastewater samples were collected, with 2,517 undergoing sequencing and submission to NCBI under the umbrella BioProject,PRJNA757291. Sequence data were released with explicit quality control (QC) tags on all sequence records, communicating our confidence in the quality of data. Variant analysis revealed wide circulation of Delta in the fall of 2021 and captured the sweep of Omicron and subsequent diversification of this lineage through the end of the sampling period. This project successfully achieved two important goals for the FDA’s GenomeTrakr program: first, contributing timely genomic data for the SARS-CoV-2 pandemic response, and second, establishing both capacity and best practices for culture-independent, population-level environmental surveillance for other pathogens of interest to the FDA. IMPORTANCE This paper serves two primary objectives. First, it summarizes the genomic and contextual data collected during a Covid-19 pandemic response project, which utilized the FDA’s laboratory network, traditionally employed for sequencing foodborne pathogens, for sequencing SARS-CoV-2 from wastewater samples. Second, it outlines best practices for gathering and organizing population-level next generation sequencing (NGS) data collected for culture-free, surveillance of pathogens sourced from environmental samples.

Microbiology↗
NASA NTRS1991

The process of control design for the NASA Langley Minimast structure

The design process used to select sensors for feedback and performance weights on the Minimast facility is discussed. Initially, a series of controllers are synthesized using H2 optimal control techniques for the given structural model, a variety of sensor locations and performance criteria to determine the best displacement sensor and/or accelerometers to be used for feedback. Upon selection of the sensors, controllers are formulated to determine the affect of using a reduced-order model of the Minimast structure instead of the higher-order structural analysis model for control design and the relationship between the actuator torque level and the closed-loop performance. Based on this information, controllers are designed using micro-synthesis techniques and implemented on the Minimast structure. Results of the implementation of these controllers on the Minimast experimental facility are presented.

Balas, Gary J.↗
NASA NTRS1997

A Disturbance Rejection Approach to Actuator and Sensor Placement

For various reasons as discussed for instance in, the selection of actuator and sensor positions is still ad hoc. This is especially true for flexible structures where many candidate configurations can exist. This study is an attempt to make the selection process more methodical. One approach to actuator and sensor placement is to optimize a closed loop performance metric directly by selecting the actuators, sensors, and controller gains simultaneously. This direct approach makes sense if the desired closed loop performance is well defined. Since the individual actuator and sensor contributions to the closed loop performance metric is complex, the solution strategy usually employs non linear programming with many design and numerical iterations. A second approach is to select actuators and/or sensors based on open loop properties so that closed loop performance is indirectly optimized. Since the individual sensor and actuator contributions to the open loop metric is simple, nonlinear optimization is usually not needed. This approach will suggest efficient actuator and sensor configurations for any type of control law. The method suggested in this study falls into the latter class of approaches.

Lim, K. B.↗
NASA NTRS2004

Te-and Zn-Doped InSb Crystals Grown in Microgravity

In 2002, within the SUBSA (Solidification Using a Baffle in Sealed Ampoules) investigation, seven doped InSb crystals were grown in microgravity at the International Space Station. The key goals of the SUBSA investigation are: (a) to clarify the origin of the melt convection in space laboratories; (b) to reduce melt convection to the level which allows reproducible diffusion-controlled segregation; (e) to explore the submerged baffle process and liquid encapsulation in microgravity. 30 crystal growth experiments were conducted in the ground unit, to optimize the design of flight ampoules and to test the transparent SUBSA furnace developed by TecMasters Inc. The specially designed furnace, allowed observation of the crystal growth process (melting, seeding, motion of the solid-liquid interface, etc.). In the summer of 2002, eight crystal growth experiments were conducted in the Microgravity Science Glovebox (MSG) facility at the ISS. Four Te-doped (k = 0.5) and three Zn-doped (k2.9) crystals were grown on undoped seeds. In one experiment, we were not able to seed and grow. The seven grown crystals were sectioned and analyzed using SIMS. The design of the SUBSA ampoules, the segregation data and the video images obtained during the SUBSA flight experiments will be presented and discussed.

Ostrogorsky, A. G.↗
NASA NTRS2004

OTIS 3.2 Software Released

Trajectory, mission, and vehicle engineers concern themselves with finding the best way for an object to get from one place to another. These engineers rely upon special software to assist them in this. For a number of years, many engineers have used the OTIS program for this assistance. With OTIS, an engineer can fully optimize trajectories for airplanes, launch vehicles like the space shuttle, interplanetary spacecraft, and orbital transfer vehicles. OTIS provides four modes of operation, with each mode providing successively stronger optimization capability. The most powerful mode uses a mathematical method called implicit integration to solve what engineers and mathematicians call the optimal control problem. OTIS 3.2, which was developed at the NASA Glenn Research Center, is the latest release of this industry workhorse and features new capabilities for parameter optimization and mission design. OTIS stands for Optimal Control by Implicit Simulation, and it is implicit integration that makes OTIS so powerful at solving trajectory optimization problems. Why is this so important? The optimization process not only determines how to get from point A to point B, but it can also determine how to do this with the least amount of propellant, with the lightest starting weight, or in the fastest time possible while avoiding certain obstacles along the way. There are numerous conditions that engineers can use to define optimal, or best. OTIS provides a framework for defining the starting and ending points of the trajectory (point A and point B), the constraints on the trajectory (requirements like "avoid these regions where obstacles occur"), and what is being optimized (e.g., minimize propellant). The implicit integration method can find solutions to very complicated problems when there is not a lot of information available about what the optimal trajectory might be. The method was first developed for solving two-point boundary value problems and was adapted for use in OTIS. Implicit integration usually allows OTIS to find solutions to problems much faster than programs that use explicit integration and parametric methods. Consequently, OTIS is best suited to solving very complicated and highly constrained problems.

Riehl, John P.↗
NASA NTRSDate not supplied

Trajectory Operations of the Artemis I Mission

This paper describes the operational design and execution of the Artemis I trajectory. It was an operationally complex trajectory with powered lunar flybys and insertion into a Distant Retrograde Orbit (DRO). A joint team of trajectory analysts at the NASA Johnson Space Center (JSC) were responsible for the design and operation of nominal and off-nominal in-space trajectories. A process was developed to convert optimized reference trajectories into Orion burn plans that could be uplinked to the vehicle. During the mission, the joint flight controller and engineering team continuously evaluated upcoming translational burns using actual vehicle conditions, monitored the trajectory for opportunities to re-optimize the trajectory in order to reduce propellant usage, and prepared for potential off-nominal scenarios. Overall Orion in-space trajectory performance is compared tomission designs to demonstrate the success of the design and operations work-flows.

Artemis I↗
NASA NTRS2006

A High-Order, Linear Time-Invariant Model for Application to Higher Harmonic Control and Flight Control System Interaction

This research describes a new methodology for the extraction of a high-order, linear time invariant model, which allows the periodicity of the helicopter response to be accurately captured. This model provides the needed level of dynamic fidelity to permit an analysis and optimization of the AFCS and HHC algorithms. The key results of this study indicate that the closed-loop HHC system has little influence on the AFCS or on the vehicle handling qualities, which indicates that the AFCS does not need modification to work with the HHC system. However, the results show that the vibration response to maneuvers must be considered during the HHC design process, and this leads to much higher required HHC loop crossover frequencies. This research also demonstrates that the transient vibration responses during maneuvers can be reduced by optimizing the closed-loop higher harmonic control algorithm using conventional control system analyses.

Cheng, Rendy P.↗
NASA NTRS1992

Dietary protein deficiency reduces lysosomal and nonlysosomal ATP-dependent proteolysis in muscle

When rats are fed a protein deficient (PD) diet for 7 days, rates of proteolysis in skeletal muscle decrease by 40-50% (N. E. Tawa, Jr., and A. L. Goldberg. Am. J. Physiol. 263 (Endocrinol. Metab. 26): E317-325, 1992). To identify the underlying biochemical adaptations, we measured different proteolytic processes in incubated muscles. The capacity for intralysosomal proteolysis, as shown by sensitivity to methylamine or lysosomal protease inhibitors, fell 55-75% in muscles from PD rats. Furthermore, extracts of muscles of PD rats showed 30-70% lower activity of many lysosomal proteases, including cathepsins B, H, and C, and carboxypeptidases A and C, as well as other lysosomal hydrolases. The fall in cathepsin B and proteolysis was evident by 3 days on the PD diet, and both returned to control levels 3 days after refeeding of the normal diet. In muscles maintained under optimal conditions, 80-90% of protein breakdown occurs by nonlysosomal pathways. In muscles of PD rats, this ATP-dependent process was also 40-60% slower. Even though overall proteolysis decreased in muscles of PD rats, their capacity for Ca(2+)-dependent proteolysis increased (by 66%), as did the activity of the calpains (+150-250%). Thus the lysosomal and the ATP-dependent processes decrease coordinately and contribute to the fall in muscle proteolysis in PD animals.

Non-NASA Center↗
NASA NTRS1991

Optimal interaction of indenter with inhomogeneous plate

Consideration is given to a new class of problems dealing with an optimal design of an inhomogeneous plate during dynamic penetration of the rigid indenter. The quality criterion of the process is defined by the specific mass of the target, which absorbs the given kinetic mass of the indenter. Parameters of control are expressed in terms of mechanical characteristics, i.e., distribution of density and the related hardness across the plate thickness. The maximum principle of Pontryagin is used to search for the piecewise continuous control function. With consideration of impact conditions and characteristics for a given class of material, an optimal target structure criterion was estimated for engineering applications.

Aptukov, Valery N.↗