Squared-error minimization with stability constraints.
Linear closed loop control system poorly damped response to deterministic inputs improved by stability constraint for minimization of mean squared error
Siljak, D. D.↗
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Optimal inputs for parameter estimation in dynamic systems with white observation noise.
Optimal deterministic inputs derived for estimating dynamic control system parameters from white observation noise
Nahi, N. E.↗
The response of cylindrical shells to random acoustic excitation over broad frequency ranges Final report
Closed cylindrical shell response for acoustic excitation random in time and deterministic in space
Bessey, R. L.↗
Ideal limiting of digital signals in Gaussian noise
Output autocorrelation properties of ideal limiters driven by binary deterministic signal plus stationary zero-mean Gaussian noise
Painter, J. H.↗
Dynamic responses of railroad car models to vertical and lateral rail inputs
Simplified dynamic models were applied in a study of vibration in a high-speed railroad car. The mathematical models used were a four-degree-of-freedom model for vertical responses to vertical rail inputs and a ten-degree-of-freedom model for lateral response to lateral or rolling (cross-level) inputs from the rails. Elastic properties of the passenger car body were represented by bending and torsion of a uniform beam. Rail-to-car (truck) suspensions were modeled as spring-mass-dashpot oscillators. Lateral spring nonlinearities approximating certain complicated truck mechanisms were introduced. The models were excited by displacement and, in some cases, velocity inputs from the rails by both deterministic (including sinusoidal) and random input functions. Results were obtained both in the frequency and time domains. Solutions in the time domain for the lateral model were obtained for a wide variety of transient and random inputs generated on-line by an analog computer. Variations in one of the damping properties of the lateral car suspension gave large fluctuations in response over a range of car speeds for a given input. This damping coefficient was significant in reducing lateral car responses that were higher for nonlinear springs for three different inputs.
Sewall, J. L.↗
Parameter identification using a creeping-random-search algorithm
A creeping-random-search algorithm is applied to different types of problems in the field of parameter identification. The studies are intended to demonstrate that a random-search algorithm can be applied successfully to these various problems, which often cannot be handled by conventional deterministic methods, and, also, to introduce methods that speed convergence to an extremal of the problem under investigation. Six two-parameter identification problems with analytic solutions are solved, and two application problems are discussed in some detail. Results of the study show that a modified version of the basic creeping-random-search algorithm chosen does speed convergence in comparison with the unmodified version. The results also show that the algorithm can successfully solve problems that contain limits on state or control variables, inequality constraints (both independent and dependent, and linear and nonlinear), or stochastic models.
Parrish, R. V.↗
Space Trajectories Error Analysis (STEAP) Programs. Volume 1: Analytic manual, update
Manual revisions are presented for the modified and expanded STEAP series. The STEAP 2 is composed of three independent but related programs: NOMAL for the generation of n-body nominal trajectories performing a number of deterministic guidance events; ERRAN for the linear error analysis and generalized covariance analysis along specific targeted trajectories; and SIMUL for testing the mathematical models used in the navigation and guidance process. The analytic manual provides general problem description, formulation, and solution and the detailed analysis of subroutines. The programmers' manual gives descriptions of the overall structure of the programs as well as the computational flow and analysis of the individual subroutines. The user's manual provides information on the input and output quantities of the programs. These are updates to N69-36472 and N69-36473.
Source record↗
On stochastic control and optimal measurement strategies
The control of stochastic dynamic systems is studied with particular emphasis on those which influence the quality or nature of the measurements which are made to effect control. Four main areas are discussed: (1) the meaning of stochastic optimality and the means by which dynamic programming may be applied to solve a combined control/measurement problem; (2) a technique by which it is possible to apply deterministic methods, specifically the minimum principle, to the study of stochastic problems; (3) the methods described are applied to linear systems with Gaussian disturbances to study the structure of the resulting control system; and (4) several applications are considered.
Kramer, L. C.↗
Development of a category 2 approach system model
An analytical model is presented which provides, as its primary output, the probability of a successful Category II approach. Typical applications are included using several example systems (manual and automatic) which are subjected to random gusts and deterministic wind shear. The primary purpose of the approach system model is to establish a structure containing the system elements, command inputs, disturbances, and their interactions in an analytical framework so that the relative effects of changes in the various system elements on precision of control and available margins of safety can be estimated. The model is intended to provide insight for the design and integration of suitable autopilot, display, and navigation elements; and to assess the interaction of such elements with the pilot/copilot.
Johnson, W. A.↗
Comments on the possibility for determining detailed atmospheric structure from transhorizon radio propagation measurements
A deterministic approach is used to examine the atmospheric structure at any instant in time, with an assumption as to the degree of anisotropy. A statistical model is also used to relate the experimental data to atmospheric structure. With this model, the three dimensional spectrum of spatial wave numbers of the refractivity fluctuations are determined, along with correlations which exist within the spectrum.
Kieburtz, R. B.↗
Synthesis of feedback systems with large plant ignorance for prescribed time domain tolerances
There is given a minimum-phase plant transfer function, with prescribed bounds on its parameter values. The plant is imbedded in a two-degree-of freedom feedback system, which is to be designed such that the system time response to a deterministic input lies within specified boundaries. Subject to the above, the design should be such as to minimize the effect of sensor noise at the input to the plant. This report presents a design procedure for this purpose, based on frequency response concepts. The time-domain tolerances are translated into equivalent frequency response tolerances. The latter lead to bounds on the loop transmission function in the form of continuous curves on the Nichols chart. The properties of the loop transmission function which satisfy these bounds with minimum effect of sensor noise, are derived.
Horowitz, I. M.↗
Control system estimation and design for aerospace vehicles with time delay
The problems of estimation and control of discrete, linear, time-varying systems are considered. Previous solutions to these problems involved either approximate techniques, open-loop control solutions, or results which required excessive computation. The estimation problem is solved by two different methods, both of which yield the identical algorithm for determining the optimal filter. The partitioned results achieve a substantial reduction in computation time and storage requirements over the expanded solution, however. The results reduce to the Kalman filter when no delays are present in the system. The control problem is also solved by two different methods, both of which yield identical algorithms for determining the optimal control gains. The stochastic control is shown to be identical to the deterministic control, thus extending the separation principle to time delay systems. The results obtained reduce to the familiar optimal control solution when no time delays are present in the system.
Allgaier, G. R.↗
Dynamic response of nonuniform structures to classes of pressure fields
A semi-analytical method is developed for the calculation of the response of nonuniform structures to deterministic and random excitation. The method is based on parametric representations of the impulse response and input functions. With these representations, a class of structures of specified geometry and a class of pressure fields of practical concern can be considered simultaneously in a single analytical calculation of structural response. In engineering applications, the parameters in the impulse response function can be fixed once the numerical solution of the associated eigenvalue problem is available; the input function parameters can be specified given a particular input function or pressure field data. This methodology is applied to nonuniform beams and circular cylindrical shells for which parametric response solutions are derived. The computerized version of these solutions is also presented.
Cottis, M. G.↗
The role and use of the stochastic linear-quadratic-Gaussian problem in control system design.
The role of the linear-quadratic stochastic control problem in engineering design is reviewed in tutorial fashion. The design approach is motivated by considering the control of a nonlinear uncertain plant about a desired input-output response. It is demonstrated how a design philosophy based on (1) deterministic perturbation control, (2) stochastic state estimation, and (3) linearized stochastic control leads to an overall closed-loop control system. The emphasis of the paper is on the philosophy of the design process, the modeling issue, and the formulation of the problem; the results are given for the sake of completeness, but no proofs are included. The systematic off-line nature of the design process is stressed throughout.
Athans, M.↗
An estimator for the standard deviation of a natural frequency. I.
A brief review of mean-square approximate systems is given. The case in which the masses are deterministic is considered first in the derivation of an estimator for the upper bound of the standard deviation of a natural frequency. Two examples presented include a two-degree-of-freedom system and a case in which the disorder in the springs is perfectly correlated. For purposes of comparison, a Monte Carlo simulation was done on a digital computer.
Schiff, A. J.↗
Design of optimal probing signals for vector parameter estimation.
In the design of optimal inputs or probing signals for parameter estimation, it is more natural to consider functions of the Fisher information matrix as the criterion of optimality instead of some function of the error covariance matrix. The input which maximizes the Fisher information measure for efficient estimation of a scalar parameter also provides the minimum error variance. The information is thus a logical choice for the optimality criterion in scalar problems. No such obvious choice is apparent for vector parameter estimation. A number of performance measures are examined and compared in the present study, and a useful criterion is selected. The design of an optimal probing signal using this criterion is shown to be equivalent to an optimal control problem in which certain equality constraints must be satisfied. This problem may be solved by conventional techniques of deterministic or stochastic optimal control.
Nahi, N. E.↗
Linear response to nonstationary random excitation.
Development of a method for computing the mean-square response of linear systems to nonstationary random excitation of the form given by y(t) = f(t) x(t), in which x(t) = a stationary process and f(t) is deterministic. The method is suitable for application to multidegree-of-freedom systems when the mean-square response at a point due to excitation applied at another point is desired. Both the stationary process, x(t), and the modulating function, f(t), may be arbitrary. The method utilizes a fundamental component of transient response dependent only on x(t) and the system, and independent of f(t) to synthesize the total response. The role played by this component is analogous to that played by the Green's function or impulse response function in the convolution integral.
Hasselman, T.↗