Calculus of variations and mathematical theory of optimal control
A bibliography is presented of publications and reports resulting from the research project.
Sagan, H.↗
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Meteorological control of lower stratospheric minor species variations - An observational example
Lower stratospheric air trajectories entering the region over Alaska at the approximately 125 mb level during late May, 1975 indicate a substantial shift in the geographical source regions for the air masses present during that time. This shift coincides with an approximately 25% decrease in the observed halocarbon mixing ratios at the 125 mb level as determined from a daily sequence of halocarbon profiles. Since the halocarbon species measured are essentially chemically inactive at this level, the observed variation is linked to the changing meteorological pattern.
Alyea, F. N.↗
Adaptive control with an expert system based supervisory level
Adaptive control is presently one of the methods available which may be used to control plants with poorly modelled dynamics or time varying dynamics. Although many variations of adaptive controllers exist, a common characteristic of all adaptive control schemes, is that input/output measurements from the plant are used to adjust a control law in an on-line fashion. Ideally the adjustment mechanism of the adaptive controller is able to learn enough about the dynamics of the plant from input/output measurements to effectively control the plant. In practice, problems such as measurement noise, controller saturation, and incorrect model order, to name a few, may prevent proper adjustment of the controller and poor performance or instability result. In this work we set out to avoid the inadequacies of procedurally implemented safety nets, by introducing a two level control scheme in which an expert system based 'supervisor' at the upper level provides all the safety net functions for an adaptive controller at the lower level. The expert system is based on a shell called IPEX, (Interactive Process EXpert), that we developed specifically for the diagnosis and treatment of dynamic systems. Some of the more important functions that the IPEX system provides are: (1) temporal reasoning; (2) planning of diagnostic activities; and (3) interactive diagnosis. Also, because knowledge and control logic are separate, the incorporation of new diagnostic and treatment knowledge is relatively simple. We note that the flexibility available in the system to express diagnostic and treatment knowledge, allows much greater functionality than could ever be reasonably expected from procedural implementations of safety nets. The remainder of this chapter is divided into three sections. In section 1.1 we give a detailed review of the literature in the area of supervisory systems for adaptive controllers. In particular, we describe the evolution of safety nets from simple ad hoc techniques, up to the use of expert systems for more advanced supervision capabilities.
Sullivan, Gerald A.↗
Singular perturbations for a Mayer variational problem
Optimal trajectory and control approximate solution by asymptotic expansion, considering Mayer variational problem solution
Kelley, H. J.↗
Dynamic verification of a digital flight control system.
Development of a digital control system dynamic variation technique which accounts for the limitation of available frequency response analyzers. Digital control system theory is briefly reviewed, and generation of the necessary theoretical frequency responses is discussed. Results of the dynamic verification of a digital control system for a Saturn V launch vehicle are presented, and attention is given to the limitations of this technique along with its applicability to other types of digital control systems. A technique for performing open-loop frequency response analyses of a flight program implemented in a 'flight-type' digital computer and interface hardware with vehicle dynamics simulated on an analog computer is described.
Nabers, J. P., Jr.↗
Photographic consulting services for earth resources program at NASA Goddard Space Flight Center
A comparison of prints from ERTS photography revealed significant differences in the image quality produced at GSFC, the EROS facility at Sioux Falls, and Eastman Kodak in Rochester. Based on this survey photographic quality was improved significantly at Sioux Falls, and improvements were suggested for optical and contact printers at the GSFC. Based on a test in which 365 meters of Eastman Electron Recording Film (ESTAR Base) SO-438 were processed the 1-sigma variation in process control from all sources is about + or - 0.04 at a density of 1.0. Variations from film and from processing were approximately equal contributors to the overall tolerance. Distortion produced by the Kodak Colorado printer at GSFC covers a range of about 0.04%, a small value compared to that caused by other factors in the ERTS system. The edge fringing inherent in the color film materials used at GSFC also seems to be a small factor in the unsharpness of ERTS color prints. MTF and granularity measurements were made on processed film samples supplied by GSFC. MTF values were above 0.70 out to 42 cycles/mm for all stages of contact printing in the ERTS system.
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Caratheodory-Hamilton-Jacobi theory in optimal control.
Caratheodory unified approach to Hamilton-Jacobi theory in variational calculus problems of optimal control
HAMILTON-JACOBI EQUATION↗
Guidance and control analysis and integration
Automation of variational methods for solution of optimum control problems, optical data sources for Mars-encounter earth-based orbit determination, and operational support equipment
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Singular optimal control and the identically non-regular problem in the calculus of variations
A small but interesting class of optimal control problems featuring a scalar control appearing linearly is equivalent to the class of identically nonregular problems in the Calculus of Variations. It is shown that a condition due to Mancill (1950) is equivalent to the generalized Legendre-Clebsch condition for this narrow class of problems.
Menon, P. K. A.↗
Variable Emissivity Through MEMS Technology
This paper discusses a new technology for variable emissivity (vari-e) radiator surfaces, which has significant advantages over traditional radiators and promises an alternative design technique for future spacecraft thermal control systems. All spacecraft rely on radiative surfaces to dissipate waste heat. These radiators have special coatings, typically with a low solar absorptivity and a high infrared-red emissivity, that are intended to optimize performance under the expected heat load and thermal sink environment. The dynamics of the heat loads and thermal environment make it a challenge to properly size the radiator and often require some means of regulating the heat rejection rate of the radiators in order to achieve proper thermal balance. Specialized thermal control coatings, which can passively or actively adjust their emissivity offer an attractive solution to these design challenges. Such systems would allow intelligent control of the rate of heat loss from a radiator in response to heat load and thermal environmental variations. Intelligent thermal control through variable emissivity systems is well suited for nano and pico spacecraft applications where large thermal fluctuations are expected due to the small thermal mass and limited electric resources. Presently there are three different types of vari-e technologies under development: Micro ElectroMechanical Systems (MEMS) louvers, Electrochromic devices, and Electrophoretic devices. This paper will describe several prototypes of micromachined (MEMS) louvers and experimental results for the emissivity variations measured on theses prototypes. It will further discuss possible actuation mechanisms and space reliability aspects for different designs. Finally, for comparison parametric evaluations of the thermal performances of the new vari-e technology and standard thermal control systems are presented in this paper.
Darrin, Ann Garrison↗
Impact of mismodeled idle engine performance on calculation and tracking of optimal 4-D descent trajectories
Advanced flight management systems are being developed which are capable of calculating optimal 3-D and 4-D flight trajectories for arbitrary fuel and time costs. These systems require mathematical models of airplane performance in order to compute the optimal profiles. Mismodeled idle engine characteristics can result in descent trajectories requiring excessive throttle and/or speedbrake activity in order to achieve the desired end conditions. This paper evaluates the cost and fuel penalties, trajectory variations, and flight control requirements associated with typical idle engine modeling errors for a twin-jet transport airplane. Variations in idle power setting, thrust, fuel flow, and surge bleed operation were evaluated for a cruise/descent flight segment. The results of this analysis provide insight into the penalties associated with uncertainties in idle engine performance and suggest methods of modeling which minimize these penalties.
Williams, D. H.↗
FM oscillator uses tetrode transistor
Tetrode-driven crystal oscillator achieves large frequency variations for a given input signal. Frequency control is obtained by variation of the second base current of the tetrode.
Boensel, D. W.↗
Set-point control of nonlinear systems
A method of nonlinear stochastic control is applied to the problem of providing set-point control. The procedure is illustrated for a nonlinear second-order plant. The controller design uses a variation of the 'multiple-model adaptive control' approach. Specific problems related to the design are investigated, including learning time and set-point accuracy dependence on the number of approximating models, chord versus tangent approximations, and the a priori Markov switching parameter values. Simulations are provided for different situations under various levels of measurement noise.
Vanlandingham, H. F.↗
Environmental parameters of the Tennessee River in Alabama. 2: Physical, chemical, and biological parameters
Physical, chemical and biological water quality data from five sites in the Tennessee River, two in Guntersville Reservoir and three in Wheeler Reservoir were correlated with climatological data for three annual cycles. Two of the annual cycles are for the years prior to the Browns Ferry Nuclear Power Plant operations and one is for the first 14 months of Plant operations. A comparison of the results of the annual cycles indicates that two distinct physical conditions in the reservoirs occur, one during the warm months when the reservoirs are at capacity and one during the colder winter months when the reservoirs have been drawn-down for water storage during the rainy months and for weed control. The wide variations of physical and chemical parameters to which the biological organisms are subjected on an annual basis control the biological organisms and their population levels. A comparison of the parameters of the site below the Power plant indicates that the heated effluent from the plant operating with two of the three reactors has not had any effect on the organisms at this site. Recommendations given include the development of prediction mathematical models (statistical analysis) for the physical and chemical parameters under specific climatological conditions which affect biological organisms. Tabulated data of chemical analysis of water and organism populations studied is given.
Rosing, L. M.↗
Adaptive stochastic control for a class of linear systems.
The problem considered in this paper deals with the control of linear discrete-time stochastic systems with unknown (possibly time-varying and random) gain parameters. The philosophy of control is based on the use of an open-loop feedback optimal (OLFO) control using a quadratic index of performance. It is shown that the OLFO system consists of (1) an identifier that estimates the system state variables and gain parameters and (2) a controller described by an 'adaptive' gain and correction term. Several qualitative properties and asymptotic properties of the OLFO adaptive system are discussed. Simulation results dealing with the control of stable and unstable third-order plants are presented. The key quantitative result is the precise variation of the control system adaptive gains as a function of the future expected uncertainty of the parameters; thus, in this problem the ordinary 'separation theorem' does not hold.
Tse, E.↗
Control law parameterization for an aeroelastic wind-tunnel model equipped with an active roll control system and comparison with experiment
Nominal roll control laws were designed, implemented, and tested on an aeroelastically-scaled free-to-roll wind-tunnel model of an advanced fighter configuration. The tests were performed in the NASA Langley Transonic Dynamics Tunnel. A parametric study of the nominal roll control system was conducted. This parametric study determined possible control system gain variations which yielded identical closed-loop stability (roll mode pole location) and identical roll response but different maximum control-surface deflections. Comparison of analytical predictions with wind-tunnel results was generally very good.
Perry, Boyd, III↗
Control law parameterization for an aeroelastic wind-tunnel model equipped with an active roll control system and comparison with experiment
Nominal roll control laws were designed, implemented, and tested on an aeroelastically-scaled free-to-roll wind-tunnel model of an advanced fighter configuration. The tests were performed in the NASA Langley Transonic Dynamics Tunnel. A parametric study of the nominal roll control system was conducted. This parametric study determined possible control system gain variations which yielded identical closed-loop stability (roll mode pole location) and identical roll response but different maximum control-surface deflections. Comparison of analytical predictions with wind-tunnel results was generally very good.
Perry, Boyd, III↗
The development of a pseudo-nyquist analysis technique for hybrid sampled-data control systems
The stability characteristics of a launch vehicle, as a function of gain and phase variations at the thrust vector controller, cannot be obtained using classical sampled-data control theory if the launch vehicle attitude control system contains both sampled-data and continuous feedback control loops. A method was developed which can be used to generate a sampled-data pseudo-Nyquist plot for gain and phase variations at the controller. This method was developed and used to determine the stability characteristics of the Saturn 1B launch vehicle in the backup guidance mode.
Burnitt, M. G.↗