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NASA NTRS1982

Interaction of a cumulus cloud ensemble with the large-scale environment. IV - The discrete model

The Arakawa-Schubert (1974) parameterization is applied to a prognostic model of large-scale atmospheric circulations and used to analyze data in a general circulation model (GCM). The vertical structure of the large-scale model and the solution for the cloud subensemble thermodynamical properties are examined to choose cloud levels and representative regions. A mass flux distribution equation is adapted to formulate algorithms for calculating the large-scale forcing and the mass flux kernel, using either direct solution or linear programming. Finally, the feedback of the cumulus ensemble on the large-scale environment for a given subensemble mass flux is calculated. All cloud subensemble properties were determined from the conservation of mass, moist static energy, and total water.

Lord, S. J.↗

NASA NTRS1982

A DSN optimal spacecraft scheduling model

A computer model is described which uses mixed-integer linear programming to provide optimal DSN spacecraft schedules given a mission set and specified scheduling requirements. A solution technique is proposed which uses Bender's Method and a heuristic starting algorithm.

Webb, W. A.↗

NASA NTRS1984

The effect of property changes on jet fuel producibility and cost

An investigation of the effect of property relaxation on jet A producibility and cost in the U.S. has been completed under NASA sponsorship by Exxon Research and Engineering Company. This presentation reviews the results obtained. Linear programming optimization models have been used. Model input included petroleum product demand and property data, estimates of crude qualities, and information on refinery processes. The time period considered was 1978 to 2010.

Varga, G. M., Jr.↗

NASA NTRS1985

An optimal spacecraft scheduling model for the NASA deep space network

Webb, W. A.↗

NASA NTRS1985

Engineering calculations for communications satellite systems planning

Computer-based techniques for optimizing communications-satellite orbit and frequency assignments are discussed. A gradient-search code was tested against a BSS scenario derived from the RARC-83 data. Improvement was obtained, but each iteration requires about 50 minutes of IBM-3081 CPU time. Gradient-search experiments on a small FSS test problem, consisting of a single service area served by 8 satellites, showed quickest convergence when the satellites were all initially placed near the center of the available orbital arc with moderate spacing. A transformation technique is proposed for investigating the surface topography of the objective function used in the gradient-search method. A new synthesis approach is based on transforming single-entry interference constraints into corresponding constraints on satellite spacings. These constraints are used with linear objective functions to formulate the co-channel orbital assignment task as a linear-programming (LP) problem or mixed integer programming (MIP) problem. Globally optimal solutions are always found with the MIP problems, but not necessarily with the LP problems. The MIP solutions can be used to evaluate the quality of the LP solutions. The initial results are very encouraging.

Reilly, C. H.↗

NASA NTRS1985

Design of suboptimal regulators for nonlinear systems

An optimal feedback control law is preferred for the regulation of a deterministic nonlinear system. In this paper, a practical, iterative design method leading to a sequence of suboptimal control laws with successively improved performance is presented. The design method requires the determination of an upper bound to the performance of each successive control law. This is obtained by solving a partial differential inequality by means of a linear programming technique. Robustness properties and the application of the design method to the control of a robot manipulator arm are also presented.

Balaram, J.↗

NASA NTRS1986

A multifunction recognition operator for telerobotic vision

Research on developing an operator capable of performing the various subtasks required of a telerobot's vision sensor is reported. The operator uses a goal-driven matching technique which is an application of a linear programming method that readily adapts to the elastic template matching approach to pattern recognition. Four applications of the operator are discussed: (1) three-space location of an isolated object; (2) shape determination of isolated planar figures; (3) image compression/restoration; and (4) shape decomposition.

Goode, P. W., IV↗

NASA NTRS1987

Optimization of orbital assignment and specification of service areas in satellite communications

The mathematical nature of the orbital and frequency assignment problem for communications satellites is explored, and it is shown that choosing the correct permutations of the orbit locations and frequency assignments is an important step in arriving at values which satisfy the signal-quality requirements. Two methods are proposed to achieve better spectrum/orbit utilization. The first, called the delta S concept, leads to orbital assignment solutions via either mixed-integer or restricted basis entry linear programming techniques; the method guarantees good single-entry carrier-to-interference ratio results. In the second, a basis for specifying service areas is proposed for the Fixed Satellite Service. It is suggested that service areas should be specified according to the communications-demand density in conjunction with the delta S concept in order to enable the system planner to specify more satellites and provide more communications supply.

Wang, Cou-Way↗

NASA NTRS1988

Optimal rejection of persistent disturbances, robust stability, and mixed sensitivity minimization

The problem of optimal disturbance rejection of bounded persistent disturbances is solved in the general nonsquare case. The minimum value of the objective function can be obtained by solving a semiinfinite linear programming problem, and an iterative procedure for obtaining approximate solutions is introduced. Application of the l1-optimal problem to robustness is discussed. A mixed sensitivity problem is formulated and shown to guarantee good disturbance rejection in the presence of plant perturbations.

Dahleh, Munther A.↗

NASA NTRS1989

Procedures for shape optimization of gas turbine disks

Two procedures, the feasible direction method and sequential linear programming, for shape optimization of gas turbine disks are presented. The objective of these procedures is to obtain optimal designs of turbine disks with geometric and stress constraints. The coordinates of the selected points on the disk contours are used as the design variables. Structural weight, stress and their derivatives with respect to the design variables are calculated by an efficient finite element method for design senitivity analysis. Numerical examples of the optimal designs of a disk subjected to thermo-mechanical loadings are presented to illustrate and compare the effectiveness of these two procedures.

Cheu, Tsu-Chien↗

NASA NTRS1989

A polynomial time algorithm for checking the robust stability of a polytope of polynomials

An efficient algorithm to check the robust stability of a polytope of polynomials is proposed. This problem is equivalent to a zero-exclusion condition at each frequency. It is shown that such a condition has to be checked at only a finite number of frequencies. This problem is formulated as a parametric linear program, which can be solved by the simplex procedure with additional computations between steps, consisting of polynomial evaluations and calculation of positive polynomial roots. The algorithm requires a finite number of steps (corresponding to frequency checks), and, in the important case of the polytope of parameters being a hypercube, this number is at most O(m3n), where n is the degree of the polynomials in the family and m is the number of parameters.

Sideris, Athanasios↗

NASA NTRS1989

Cooperative control of two active spacecraft during proximity operations

A cooperative autopilot is developed for the control of the relative attitude, relative position and absolute attitude of two maneuvering spacecraft during on orbit proximity operations. The autopilot consists of an open-loop trajectory solver which computes a nine dimensional linearized nominal state trajectory at the beginning of each maneuver and a phase space regulator which maintains the two spacecraft on the nominal trajectory during coast phases of the maneuver. A linear programming algorithm is used to perform jet selection. Simulation tests using a system of two space shuttle vehicles are performed to verify the performance of the cooperative controller and comparisons are made to a traditional passive target/active pursuit vehicle approach to proximity operations. The cooperative autopilot is shown to be able to control the two vehicle system when both the would be pursuit vehicle and the target vehicle are not completely controllable in six degrees of freedom. The cooperative controller is also shown to use as much as 37 percent less fuel and 57 percent fewer jet firings than a single pursuit vehicle during a simple docking approach maneuver.

Polutchko, Robert J.↗

NASA NTRS1990

Optimal fabrication processes for unidirectional metal-matrix composites: A computational simulation

A method is proposed for optimizing the fabrication process of unidirectional metal matrix composites. The temperature and pressure histories are optimized such that the residual microstresses of the composite at the end of the fabrication process are minimized and the material integrity throughout the process is ensured. The response of the composite during the fabrication is simulated based on a nonlinear micromechanics theory. The optimal fabrication problem is formulated and solved with non-linear programming. Application cases regarding the optimization of the fabrication cool-down phases of unidirectional ultra-high modulus graphite/copper and silicon carbide/titanium composites are presented.

Saravanos, D. A.↗

NASA NTRS1989

Time optimal movement of cooperating robots

The maximization of the speed of movement along a prescribed path, of the system formed by a set of robot arms and the object they hold is examined. The actuator torques that maximize the acceleration of the system are shown to be determined by the solution to a standard linear programming problem. The combination of this result with the known control strategy for time optimal movement of a single robot arm yields an algorithm for time optimal movement of multiple robot arms holding the same workpiece.

Mccarthy, J. M.↗

NASA NTRS1990

Probabilistic structural analysis by extremum methods

The objective is to demonstrate discrete extremum methods of structural analysis as a tool for structural system reliability evaluation. Specifically, linear and multiobjective linear programming models for analysis of rigid plastic frames under proportional and multiparametric loadings, respectively, are considered. Kinematic and static approaches for analysis form a primal-dual pair in each of these models and have a polyhedral format. Duality relations link extreme points and hyperplanes of these polyhedra and lead naturally to dual methods for system reliability evaluation.

Nafday, Avinash M.↗

NASA NTRS1991

l1-optimal control of multivariable systems with output norm constraints

This paper considers the l1-optimal control problem for general rational plants. It is shown that, for plants with no poles or zeros on the unit circle, an optimal compensator exists and that the resulting closed loop transfer function is polynomial whenever there are at least as many controls as regulated outputs and at least as many measurements as exogeneous inputs. Exactly or approximately, optimal rational compensators can be obtained by solving a sequence of finite linear programs for the coefficients of a polynomial closed-loop transfer function. No assumptions on plant poles or zeros are required to obtain at least approximately optimal compensators. It is shown that constrained problems in which a set of outputs is regulated subject to l(infinity)-norm constraints on another set of outputs can be solved using a slight modification of the same algorithm.

Mcdonald, J. S.↗

NASA NTRS1992

Mathematical analysis techniques for modeling the space network activities

The objective of the present work was to explore and identify mathematical analysis techniques, and in particular, the use of linear programming. This topic was then applied to the Tracking and Data Relay Satellite System (TDRSS) in order to understand the space network better. Finally, a small scale version of the system was modeled, variables were identified, data was gathered, and comparisons were made between actual and theoretical data.

Foster, Lisa M.↗

NASA NTRS1990

Optimal rejection of bounded persistent disturbances in periodic systems

The problem of optimal rejection of bounded persistent disturbances is solved in the case of linear discrete-time period systems. The solution consists of solving an equivalent time-invariant standard l1 optimization problem subject to an additional constraint. This constraint ensures the causality of the resulting periodic controller. By the duality theory, the problem is shown to be equivalent to a linear programming problem, which is no harder than the standard l1 problem.

Dahleh, Munther A.↗