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Optimization problems involving linear systems with retardations in the controls are studied in a systematic way. Some physical motivation for the problems is discussed. The topics covered are: controllability, existence and uniqueness of the optimal control, sufficient conditions, techniques of synthesis, and dynamic programming. A number of solved examples are presented.
A simple heuristic algorithm for designing highly reliable modularly redundant computer systems under complexity constraints is presented. The technique, which produces near optimal solutions, is intuitively appealing and easy to apply. The algorithms performance is shown to compare very well with the optimal solution obtained via a computerized model for dynamic programming.
This paper summarizes the most current configuration of the Solar Electric Propulsion Stage (SEPS) design resulting from the synthesis of key tradeoff analyses. The baseline SEPS is a 21-kW propulsion-power vehicle using the Shuttle/Interim Upper Stage (IUS) launch vehicle for planetary and geosynchronous missions. The trade analyses supporting the baseline configuration include ion thruster array pattern, solar array stowage concepts, and number of thrusters and power processors (PP). In addition, an integrated thermal control and structural system was optimized and designed to meet flight loads and dynamics requirements. Payload provisions, mercury propellant refueling, and design compatibility of the SEPS and Shuttle/IUS are presented.
Results are presented to illustrate the application of established procedures of linear, quadratic, Gaussian optimal estimation and control to a spacecraft with dynamically significant elastic appendages. Interpretations are provided in both time domain and frequency domain, and conclusions are drawn for a wide class of problems of flexible spacecraft attitude control.
Basic research on the engineering behavior of large space structures is presented. Methods of structural analysis, control, and optimization of large flexible systems are examined. Topics of investigation include the Load Correction Method (LCM) modeling technique, stabilization of flexible bodies by feedback control, mathematical refinement of analysis equations, optimization of the design of structural components, deployment dynamics, and the use of microprocessors in attitude and shape control of large space structures. Information on key personnel, budgeting, support plans and conferences is included.
An algorithm for maximum likelihood (ML) estimation is developed primarily for multivariable dynamic systems. The algorithm relies on a new optimization method referred to as a modified Newton-Raphson with estimated sensitivities (MNRES). The method determines sensitivities by using slope information from local surface approximations of each output variable in parameter space. The fitted surface allows sensitivity information to be updated at each iteration with a significant reduction in computational effort compared with integrating the analytically determined sensitivity equations or using a finite-difference method. Different surface-fitting methods are discussed and demonstrated. Aircraft estimation problems are solved by using both simulated and real-flight data to compare MNRES with commonly used methods; in these solutions MNRES is found to be equally accurate and substantially faster. MNRES eliminates the need to derive sensitivity equations, thus producing a more generally applicable algorithm.
A quasi-harmonic-lattice-dynamics method coupled with a pattern-recognition optimization scheme is used to determine the minimum energy structures and magnetic orientations of solid oxygen. It is shown that the magnetic interaction is responsible for the stability of alpha-O2 with respect to beta-O2 at zero temperature and pressure. The calculated alpha-O2 lattice parameters, magnetic orientations, and sublimation energy are in good agreement with experiment. Phonon dispersion curves are calculated at vector k not equal to zero and the acoustic sound velocities are determined. The rms translational and orientational fluctuations from equilibrium are also calculated. The beta-O2 phase is described by constraining the magnetic moments so that the magnetic Hamiltonian preserves the hexagonal symmetry of the crystal. The calculated lattice parameters are in good agreement with the experiments, and a three-sublattice, quasi-helical magnetic orientation is predicted from structural and energetic considerations.
The topics of research in this program include pilot/vehicle analysis techniques, identification of pilot dynamics, and control and display synthesis techniques for optimizing aircraft handling qualities. The project activities are discussed. The current technical activity is directed at extending and validating the active display synthesis procedure, and the pilot/vehicle analysis of the NLR rate-command flight configurations in the landing task. Two papers published by the researchers are attached as appendices.
The reanalysis of non-self-adjoint dynamic models is computationally very expensive in design optimization applications. This paper describes several approximations that can be applied to eigenvalues of non-hermitian matrices to reduce that computational cost. Approximations based on eigenvalue derivatives, generalized Rayleigh quotient and the trace theorem are presented and their accuracy and computational cost are estimated. The accuracy and cost estimates are verified by applying the approximations to random matrices and matrices arising in flutter analysis of compressor blades. Recommendations are made for selection of the best approximation when the derivatives are available and when they are not. In particular, it is concluded that the quadratic approximation for eigenvalues should never be used as higher order approximations are always more accurate as well as more efficient.
The problem of continuous low-thrust planar orbit transfer of large flexible structures is formulated as an optimal control problem with terminal state constraints. The dynamics of the spacecraft motion are treated as a point-mass central force field problem; the thrust-acceleration magnitude is treated as an additional state variable; and the rate of change of thrust-acceleration is treated as a control variable. To ensure smooth transfer, essential for flexible structures, an additional quadratic term is appended to the time cost functional. This term penalizes any abrupt change in acceleration. Numerical results are presented for the special case of a planar transfer.
A computer-aiding concept for low-altitude helicopter flight was developed and evaluated in a real-time piloted simulation. The concept included an optimal control trajectory-generated algorithm based on dynamic programming, and a head-up display (HUD) presentation of a pathway-in-the-sky, a phantom aircraft, and flight-path vector/predictor symbol. The trajectory-generation algorithm uses knowledge of the global mission requirements, a digital terrain map, aircraft performance capabilities, and advanced navigation information to determine a trajectory between mission waypoints that minimizes threat exposure by seeking valleys. The pilot evaluation was conducted at NASA Ames Research Center's Sim Lab facility in both the fixed-base Interchangeable Cab (ICAB) simulator and the moving-base Vertical Motion Simulator (VMS) by pilots representing NASA, the U.S. Army, and the U.S. Air Force. The pilots manually tracked the trajectory generated by the algorithm utilizing the HUD symbology. They were able to satisfactorily perform the tracking tasks while maintaining a high degree of awareness of the outside world.
A computer-aiding concept for low-altitude helicopter flight was developed and evaluated in a real-time piloted simulation. The concept included an optimal control trajectory-generated algorithm based on dynamic programming, and a head-up display (HUD) presentation of a pathway-in-the-sky, a phantom aircraft, and flight-path vector/predictor symbol. The trajectory-generation algorithm uses knowledge of the global mission requirements, a digital terrain map, aircraft performance capabilities, and advanced navigation information to determine a trajectory between mission waypoints that minimizes threat exposure by seeking valleys. The pilot evaluation was conducted at NASA Ames Research Center's Sim Lab facility in both the fixed-base Interchangeable Cab (ICAB) simulator and the moving-base Vertical Motion Simulator (VMS) by pilots representing NASA, the U.S. Army, and the U.S. Air Force. The pilots manually tracked the trajectory generated by the algorithm utilizing the HUD symbology. They were able to satisfactorily perform the tracking tasks while maintaining a high degree of awareness of the outside world.
A computer aiding concept for low-altitude helicopter flight has been developed and evaluated in a real-time piloted simulation. The concept included an optimal control trajectory-generation algorithm based upon dynamic programming, and a helmet-mounted display (HMD) presentation of a pathway-in-the-sky, a phantom aircraft, and flight-path vector/predictor guidance symbology. The pilot evaluation was conducted at the NASA-Ames Research Center moving base vertical motion simulator (VMS) by pilots representing NASA, the US Army, Air Force, and helicopter industry. The pilot manually tracked the trajectory generated by the algorithm utilizing the HMD symbology. The pilots were able to satisfactorily perform the tracking tasks while maintaining a high degree of awareness of the outside world.
A computer aiding concept for low-altitude helicopter flight was developed and evaluated in a real-time piloted simulation. The concept included an optimal control trajectory-generation algorithm based upon dynamic programming and a helmet-mounted display (HMD) presentation of a pathway-in-the-sky, a phantom aircraft, and flight-path vector/predictor guidance symbology. The trajectory-generation algorithm uses knowledge of the global mission requirements, a digital terrain map, aircraft performance capabilities, and advanced navigation information to determine a trajectory between mission way points that seeks valleys to minimize threat exposure. The pilot evaluation was conducted at NASA ARC moving base Vertical Motion Simulator (VMS) by pilots representing NASA, the U.S. Army, the Air Force, and the helicopter industry. The pilots manually tracked the trajectory generated by the algorithm utilizing the HMD symbology. The pilots were able to satisfactorily perform the tracking tasks while maintaining a high degree of awareness of the outside world.
Designing missions on expendable launch vehicles (ELV's) includes determining launch vehicle performance capabilities and trajectory characteristics over the range of mission requirements for suitable launch periods. This analysis depends on mathematically modeling both the launch vehicle and the mission requirements. Generally the result is a mathematical model that is described by an objective function to be optimized subject to an assortment of algebraic and dynamic constraints. About 30 years ago, engineers at Lewis Research Center (LeRC) undertook the task of creating a software code to solve 3D versions of such problems and based it on the Calculus of Variations/Optimal Control Theory. One of these codes, DUKSUP, has been in use at LeRC for nearly 25 years, during which time it has played an important role in a large number of studies and actual missions. Currently it is being used by about 12 analysts in the Center's Advanced Space Analysis Office (ASAO) to do mission design, feasibility studies, corroboration of contractor data and planning studies for the Space Exploration Initiative (SEI). Today, it is one of the few ELV mission analysis production codes based on variational methods. With future ELV missions in mind, ASAO is presently creating a new code to upgrade DUKSUP's capabilities.
To realize accurate two-color differential measurements, an image digitizing system with variable spatial resolution was designed, built, and integrated to a photon-counting picosecond streak camera, yielding a temporal scan resolution better than 300 femtosecond/pixel. The streak camera is configured to operate with 3 spatial channels; two of these support green (532 nm) and uv (355 nm) while the third accommodates reference pulses (764 nm) for real-time calibration. Critical parameters affecting differential timing accuracy such as pulse width and shape, number of received photons, streak camera/imaging system nonlinearities, dynamic range, and noise characteristics were investigated to optimize the system for accurate differential delay measurements. The streak camera output image consists of three image fields, each field is 1024 pixels along the time axis and 16 pixels across the spatial axis. Each of the image fields may be independently positioned across the spatial axis. Two of the image fields are used for the two wavelengths used in the experiment; the third window measures the temporal separation of a pair of diode laser pulses which verify the streak camera sweep speed for each data frame. The sum of the 16 pixel intensities across each of the 1024 temporal positions for the three data windows is used to extract the three waveforms. The waveform data is processed using an iterative three-point running average filter (10 to 30 iterations are used) to remove high-frequency structure. The pulse pair separations are determined using the half-max and centroid type analysis. Rigorous experimental verification has demonstrated that this simplified process provides the best measurement accuracy. To calibrate the receiver system sweep, two laser pulses with precisely known temporal separation are scanned along the full length of the sweep axis. The experimental measurements are then modeled using polynomial regression to obtain a best fit to the data. Data aggregation using normal point approach has provided accurate data fitting techniques and is found to be much more convenient than using the full rate single shot data. The systematic errors from this model have been found to be less than 3 ps for normal points.
Four-dimensional data assimilation strategies can generally be classified as either current or next generation, depending upon whether they are used operationally or not. Current-generation data-assimilation techniques are those that are presently used routinely in operational-forecasting or research applications. They can be classified into the following categories: intermittent assimilation, Newtonian relaxation, and physical initialization. It should be noted that these techniques are the subject of continued research, and their improvement will parallel the development of next generation techniques described by the other speakers. Next generation assimilation techniques are those that are under development but are not yet used operationally. Most of these procedures are derived from control theory or variational methods and primarily represent continuous assimilation approaches, in which the data and model dynamics are 'fitted' to each other in an optimal way. Another 'next generation' category is the initialization of convective-scale models. Intermittent assimilation systems use an objective analysis to combine all observations within a time window that is centered on the analysis time. Continuous first-generation assimilation systems are usually based on the Newtonian-relaxation or 'nudging' techniques. Physical initialization procedures generally involve the use of standard or nonstandard data to force some physical process in the model during an assimilation period. Under the topic of next-generation assimilation techniques, variational approaches are currently being actively developed. Variational approaches seek to minimize a cost or penalty function which measures a model's fit to observations, background fields and other imposed constraints. Alternatively, the Kalman filter technique, which is also under investigation as a data assimilation procedure for numerical weather prediction, can yield acceptable initial conditions for mesoscale models. The third kind of next-generation technique involves strategies to initialize convective scale (non-hydrostatic) models.
The ever present demand for reduced flight times has renewed interest in High Speed Civil Transports (HSCT). The need for an HSCT becomes especially apparent when the long distance, over-sea, high growth Pacific rim routes are considered. Crucial to any successful HSCT design are minimal environmental impact and economic viability. Vital is the transport's aerodynamic efficiency, ultimately effecting both the environmental impact and the operating cost. Optimization, including numerical optimization, coupled with the use of computational fluid dynamics (CFD) technology, has and will offer a significant improvement beyond traditional methods.