The Control of Nonlinear Stochastic Control Systems Under Discounted Performance Criteria
Finite Markov chain control and numerical algorithm for optimal control
Harris, C. A.↗
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The control of nonlinear stochastic control systems under discounted performance criteria
Control algorithm for optimization of nonlinear stochastic processes with discounted performance criteria
Harris, C. A.↗
Navigation for space shuttle approach and landing using an inertial navigation system augmented by data from a precision ranging system or a microwave scan beam landing guidance system
A preliminary study has been made of the navigation performance which might be achieved for the high cross-range space shuttle orbiter during final approach and landing by using an optimally augmented inertial navigation system. Computed navigation accuracies are presented for an on-board inertial navigation system augmented (by means of an optimal filter algorithm) with data from two different ground navigation aids; a precision ranging system and a microwave scanning beam landing guidance system. These results show that augmentation with either type of ground navigation aid is capable of providing a navigation performance at touchdown which should be adequate for the space shuttle. In addition, adequate navigation performance for space shuttle landing is obtainable from the precision ranging system even with a complete dropout of precision range measurements as much as 100 seconds before touchdown.
Mcgee, L. A.↗
A summary report on system effectiveness and optimization study
Report treats optimization and effectiveness separately. Report illustrates example of dynamic programming solution to system optimization. Computer algorithm has been developed to solve effectiveness problem and is included in report.
Williamson, O. L.↗
Panel flutter optimization by gradient projection
A gradient projection optimal control algorithm incorporating conjugate gradient directions of search is described and applied to several minimum weight panel design problems subject to a flutter speed constraint. New numerical solutions are obtained for both simply-supported and clamped homogeneous panels of infinite span for various levels of inplane loading and minimum thickness. The minimum thickness inequality constraint is enforced by a simple transformation of variables.
Pierson, B. L.↗
Research on an augmented Lagrangian penalty function algorithm for nonlinear programming
The augmented Lagrangian (ALAG) Penalty Function Algorithm for optimizing nonlinear mathematical models is discussed. The mathematical models of interest are deterministic in nature and finite dimensional optimization is assumed. A detailed review of penalty function techniques in general and the ALAG technique in particular is presented. Numerical experiments are conducted utilizing a number of nonlinear optimization problems to identify an efficient ALAG Penalty Function Technique for computer implementation.
Frair, L.↗
A study of the application of singular perturbation theory
A hierarchical real time algorithm for optimal three dimensional control of aircraft is described. Systematic methods are developed for real time computation of nonlinear feedback controls by means of singular perturbation theory. The results are applied to a six state, three control variable, point mass model of an F-4 aircraft. Nonlinear feedback laws are presented for computing the optimal control of throttle, bank angle, and angle of attack. Real Time capability is assessed on a TI 9900 microcomputer. The breakdown of the singular perturbation approximation near the terminal point is examined Continuation methods are examined to obtain exact optimal trajectories starting from the singular perturbation solutions.
Mehra, R. K.↗
Optimal analytic rendezvous using Clohessy-Wiltshire equations
The optimal solution time that minimizes the sum of the two applied impulses necessary to rendezvous is obtained analytically for the Clohessy-Wiltshire equations with a linear gravity model assumption. A plume impingement inequality constraint on the solution is examined, and an optimal policy is developed. Numerical tests are conducted to verify the analysis and to illustrate the optimal solution algorithm.
Jezewski, D. J.↗
Optimal control of sun tracking solar concentrators
Application of the modern control theory to derive an optimal sun tracking control for a point focusing solar concentrator is presented. A standard tracking problem converted to regulator problem using a sun rate input achieves an almost zero steady state tracking error with the optimal control formulation. However, these control techniques are costly because optimal type algorithms require large computing systems, thus they will be used mainly as comparison standards for other types of control algorithms and help in their development.
Hughes, R. O.↗
An analytic approach to optimal rendezvous using Clohessy-Wiltshire equations
An analytic approach is used to obtain the optimal solution time that minimizes the sum of the two applied impulses necessary to rendezvous for the Clohessy-Wiltshire equations. A plume impingement inequality constraint on the solution is examined, and an optimal policy is developed. Numerical tests are conducted to verify the analysis and to illustrate the optimal solution algorithm.
Jezewski, D. J.↗
Automated design using numerical optimization
Numerical optimization concepts are described with limited technical detail. The purpose is to provide the nonspecialist with sufficient information to judge the applicability of these methods to his particular design problem. The concepts are first described in physical terms to give a basic understanding of the iterative procedure employed by these methods. Next, the typical engineering task is presented and converted to a form ammenable to solution by numerical optimization. Basic algorithms for solving this problem are identified. Numerous applications are referenced, emphasizing the structural design discipline. The state of the art allows for the routine solution of nonlinear design problems of approximately 20 independent variables subject to 100 or more constraints. In many applications, much larger design problems may be solved. Selected references are provided which describe the methods and applications in more detail.
Vanderplaats, G. N.↗
Optimum damper locations for a free-free beam
Algorithms to optimally locate and design dampers for large space structures were developed. The requirements for distributed sensing and actuation in control of structural systems were determined. Mathematical programming was used to solve for optimum damping rate and location. Actuator dynamics were considered to solve for optimum actuator mass.
Horner, G. C.↗
Ship and satellite bio-optical research in the California Bight
Mesoscale biological patterns and processes in productive coastal waters were studied. The physical and biological processes leading to chlorophyll variability were investigated. The ecological and evolutionary significance of this variability, and its relation to the prediction of fish recruitment and marine mammal distributions was studied. Seasonal primary productivity (using chlorophyll as an indication of phytoplankton biomass) for the entire Southern California Bight region was assessed. Complementary and contemporaneous ship and satellite (Nimbus 7-CZCS) bio-optical data from the Southern California Bight and surrounding waters were obtained and analyzed. These data were also utilized for the development of multi-platform sampling strategies and the optimization of algorithms for the estimation of phytoplankton biomass and primary production from satellite imagery.
Smith, R. C.↗
ORACLS - A linear-quadratic-Gaussian computer-aided design package
ORACLS, an acronym denoting Optimal Regular Algorithms for the Control of Linear Systems, is a collection of FORTRAN coded subroutines dedicated to the formulation and solution of the Linear-Quadratic-Gaussian (LQG) design problem modeled in both continuous and discrete form. The ORACLS system is under continuous development at the NASA Langley Research Center, Hampton, Virginia, and is widely used by universities and industry within the U.S.A. The current (operational) ORACLS version as well as new software under development is described.
Armstrong, E. S.↗
Algorithm Solves Constrained and Unconstrained Optimization Problems
Is quasi-Newton iteration utilizing Broyden/Fletcher/Goldfarb/Shanno update on inverse Hessian matrix. Capable of solving constrained optimization unconstrained optimization and constraints only problems with one to five independent variables from one to five constraint functions and one dependent function optimized.
Denson, M. A.↗
Eigenvalue Placement and Stabilization by Constrained Optimization
A pole placement algorithm is proposed which uses constrained nonlinear optimization techniques on a finite dimensional model of a linear n degree of freedom system. Low order feedback control is assumed where r poles may be assigned; r being the rank of the sensor coefficient matrix. It is shown that by combining feedback control theory methods with optimization techniques, one can ensure the stability characteristics of a system, and can alter its transient response.
Decaro, S. M.↗
Safe microburst penetration techniques: A deterministic, nonlinear, optimal control approach
A relatively large amount of computer time was used for the calculation of a optimal trajectory, but it is subject to reduction with moderate effort. The Deterministic, Nonlinear, Optimal Control algorithm yielded excellent aircraft performance in trajectory tracking for the given microburst. It did so by varying the angle of attack to counteract the lift effects of microburst induced airspeed variations. Throttle saturation and aerodynamic stall limits were not a problem for the case considered, proving that the aircraft's performance capabilities were not violated by the given wind field. All closed loop control laws previously considered performed very poorly in comparison, and therefore do not come near to taking full advantage of aircraft performance.
Psiaki, Mark L.↗
Recent developments in FEM-CFD
The current status of CFD with regard to unstructured grids employing finite element methods and Eulerian frames is reviewed. Algorithms suitable for the computation of large three-dimensional problems involving flow past arbitrary geometries are developed. Adaptive mesh refinement strategy is reviewed, and domain splitting or local time-stepping are briefly addressed. The development of search algorithms of optimal order, variable time-stepping Jacobi smoothers for elliptic problems, and transport concepts for hyperbolics to help achieve good performance for unstructured multigrid processes is discussed. As examples, transient supersonic flow in a channel, regular shock reflection of a wall, viscous flow past a protruberance, potential flow past a cylinder, and Burgers equation are considered.
Loehner, R.↗