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Computer program constructs a sequence of optimal solutions to dynamically-approximate linear equations. Specification of the number and type of subarcs in the optimal solution allows simultaneous satisfaction of all switching criteria.
Simultaneous estimation of state and noise statistics in linear dynamical systems using optimal procedure
Constrained optimization procedure for deriving linear estimator of population mean in rotation sampling
Algorithm for fixed time minimum energy discrete optimal control problems of linear plants with convex constraints imposed on terminal state
Dual type method solving discrete optimal control problems with linear plants, convex cost and constraint taking into account dynamic structure
Combined optimal estimation and control techniques are applied for the first time to satellite tracking systems. Both radio antenna and optical tracking systems of NASA are considered. The optimal estimation is accomplished using an extended Kalman filter resulting in an estimated state of the satellite and of the tracking system. This estimated state constitutes an input to the optimal controller. The optimal controller treats a linearized system with a quadratic performance index. The maximum principle is applied and a steady-state approximation to the resulting Riccati equation is obtained. A computer program, RATS, implementing this algorithm is described. A feasibility study of real-time implementation, tracking simulations, and parameter sensitivity studies are also reported.
CONMIN is a FORTRAN program, in subroutine form, for the solution of linear or nonlinear constrained optimization problems. The basic optimization algorithm is the Method of Feasible Directions. The user must provide a main calling program and an external routine to evaluate the objective and constraint functions and to provide gradient information. If analytic gradients of the objective or constraint functions are not available, this information is calculated by finite difference. While the program is intended primarily for efficient solution of constrained problems, unconstrained function minimization problems may also be solved, and the conjugate direction method of Fletcher and Reeves is used for this purpose. This manual describes the use of CONMIN and defines all necessary parameters. Sufficient information is provided so that the program can be used without special knowledge of optimization techniques. Sample problems are included to help the user become familiar with CONMIN and to make the program operational.
The Federal Aviation Administration has initiated a program to automate its existing manual air traffic handling procedures. One procedure, whose automation is expected to increase controller efficiency by 2.6 to 2.9 times, is known as aircraft merging. This procedure is concerned with the merging of N aircraft, which are distributed among K feeder routes, into one or more final routes. The question of obtaining an exactly realizable and easily implementable automatic controller for merging is discussed. The optimal control of a linear system with state and control constraints is considered.
Mathematical and philosophical approaches are presented for evaluation and implementation of ground and air transportation systems. Basic decision processes are examined that are used for cost analyses and planning (i.e, statistical decision theory, linear and dynamic programming, optimization, game theory). The effects on the environment and the community that a transportation system may have are discussed and modelled. Algorithmic structures are examined and selected bibliographic annotations are included. Transportation dynamic models were developed. Citizen participation in transportation projects (i.e, in Maryland and Massachusetts) is discussed. The relevance of the modelling and evaluation approaches to air transportation (i.e, airport planning) is examined in a case study in St. Louis, Missouri.
A numerical technique is given for solving the matrix quadratic equation that arises in the optimal stationary control of linear systems with state (and/or control) dependent noise. The technique exploits fully existing, efficient algorithms for the matrix Lyapunov and Ricatti equations. The computational requirements are discussed, with an associated example.
Control-theory design package aids design of linear-quadratic-Gaussian (LOG) controllers and optimal filters. It is applicable to systems that can be modeled by linear time-invariant differential or difference equations.
An attempt is made to establish a connection between linear multistep methods for applications to ordinary differential equations and their extension (by approximate factorization) to alternating direction implicit methods for partial differential equations. An earlier implicit factored scheme for the compressible Navier-Stokes equations is generalized by innovations that (1) increase the class of temporal difference schemes to include all linear multistep methods, (2) optimize the class of unconditionally stable factored schemes by a new choice of unknown variable, and (3) improve the computational efficiency by the introduction of quasi-one-leg methods.
A scheme for the control and maneuvering of a large flexible spacecraft by means of two flexible AMCD's using noncontacting magnetic suspension is presented. The system consists of a flexible vehicle, two flexible rings and a magnetic suspension and driving assembly. The necessary skewing of the rings for maneuvering of the vehicle is accomplished by moving the pairs of magnets along tracks distributed around the circumference of the vehicle. The equations of motion for each subsystem are derived by the Lagrangian approach. Attitude motions are described in terms of quasi-coordinates. For small vehicle angular rates and rings attitude motions, an ordering scheme can be used to separate the equations of motion according to the magnitude of the terms. The ordered equations of motion lead to a linear time-variant optimal control problem for the maneuvering of the spacecraft.
Major features of SYNPAC (Synthesis Package for Active Controls) are described. SYNPAC employs constrained optimization techniques which allow explicit inclusion of design criteria (constraints) in the control law design process. Interrelationships are indicated between this constrained optimization approach, classical and linear quadratic Gaussian design techniques. Results are presented that were obtained by applying SYNPAC to the design of a combined stability augmentation/gust load alleviation control law for the DAST ARW-2.
In many applications, it is useful to have information regarding the effect of the perturbations of the design problem constants (parameters) on the optimum solution of the problem. Sobieszczanski-Sobieski et al. (1981) have, therefore, proposed to utilize an optimum sensitivity analysis as a structural design tool to assess the parameter perturbation effects by extrapolations based on optimum sensitivity derivatives. The present investigation is concerned with an example of optimum sensitivity analysis involving a composite panel. The case was selected in connection with the nonlinearity of the constraints and, the tendency for a set of active constraints to change when the parameters are disturbed. Under these adverse conditions, sensitivity derivatives are used in linear extrapolations to extend optimization information over a limited range of variation for a typical parameter.
The scalloping problem for the case of Gaussian noise statistics is analyzed. The optimal weighting strategy for linearly combining two observations in adjacent beam areas is derived, and the sensitivity and scalloping for this weighting strategy are compared with those realized using a single observation or using equal weighting of two observations. The variation of the probability for detecting ETI signals with scan separation are calculated for the various weighting strategies, assuming that the transmitters are of equal strength and are uniformly distributed throughout space.
The Chandrasekhar equations arising in optimal control problems for linear distributed parameter systems are considered. The equations are derived via approximation theory. This approach is used to obtain existence, uniqueness, and strong differentiability of the solutions and provides the basis for a convergent computation scheme for approximating feedback gain operators. A numerical example is presented to illustrate these ideas.
The minimum weight design of a helicopter rotor blade subject to constraints on coupled flap-lag natural frequencies has been studied. A constraint has also been imposed on the minimum value of the autorotational inertia of the blade in order to ensure that it has sufficient inertia to autorotate in the case of engine failure. The program CAMRAD is used for the blade modal analysis and CONMIN is used for the optimization. In addition, a linear approximation analysis involving Taylor series expansion has been used to reduce the analysis effort. The procedure contains a sensitivity analysis which consists of analytical derivatives of the objective function and the autorotational inertia constraint and central finite difference derivatives of the frequency constraints. Optimum designs have been obtained for both rectangular and tapered blades. Design variables include taper ratio, segment weights, and box beam dimensions. It is shown that even when starting with an acceptable baseline design, a significant amount of weight reduction is possible while satisfying all the constraints for both rectangular and tapered blades.