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.↗
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Studies of thrust vector control of large space vehicles Final report
Display systems, fluid amplification techniques, stochastic processes, and thrust vector control systems
Boland, J. S., III↗
Differential geometric methods in system theory.
Discussion of certain problems in system theory which have been or might be solved using some basic concepts from differential geometry. The problems considered involve differential equations, controllability, optimal control, qualitative behavior, stochastic processes, and bilinear systems. The main goal is to extend the essentials of linear theory to some nonlinear classes of problems.
Brockett, R. W.↗
An adaptive technique for a redundant-sensor navigation system.
An on-line adaptive technique is developed to provide a self-contained redundant-sensor navigation system with a capability to utilize its full potentiality in reliability and performance. This adaptive system is structured as a multistage stochastic process of detection, identification, and compensation. It is shown that the detection system can be effectively constructed on the basis of a design value, specified by mission requirements, of the unknown parameter in the actual system, and of a degradation mode in the form of a constant bias jump. A suboptimal detection system on the basis of Wald's sequential analysis is developed using the concept of information value and information feedback. The developed system is easily implemented, and demonstrates a performance remarkably close to that of the optimal nonlinear detection system. An invariant transformation is derived to eliminate the effect of nuisance parameters such that the ambiguous identification system can be reduced to a set of disjoint simple hypotheses tests. By application of a technique of decoupled bias estimation in the compensation system the adaptive system can be operated without any complicated reorganization.
Chien, T.-T.↗
Reflectance of vegetation, soil, and water
There are no author-identified significant results in this report. This report deals with the selection of the best channels from the 24-channel aircraft data to represent crop and soil conditions. A three-step procedure has been developed that involves using univariate statistics and an F-ratio test to indicate the best 14 channels. From the 14, the 10 best channels are selected by a multivariate stochastic process. The third step involves the pattern recognition procedures developed in the data analysis plan. Indications are that the procedures in use are satsifactory and will extract the desired information from the data.
Wiegand, C. L.↗
Control theory for random systems
A survey is presented of the current knowledge available for designing and predicting the effectiveness of controllers for dynamic systems which can be modeled by ordinary differential equations. A short discussion of feedback control is followed by a description of deterministic controller design and the concept of system state. The need for more realistic disturbance models led to the use of stochastic process concepts, in particular the Gauss-Markov process. A compensator controlled system, with random forcing functions, random errors in the measurements, and random initial conditions, is treated as constituting a Gauss-Markov random process; hence the mean-square behavior of the controlled system is readily predicted. As an example, a compensator is designed for a helicopter to maintain it in hover in a gusty wind over a point on the ground.
Bryson, A. E., Jr.↗
Power spectral density estimation by spline smoothing in the frequency domain
An approach, based on a global averaging procedure, is presented for estimating the power spectrum of a second order stationary zero-mean ergodic stochastic process from a finite length record. This estimate is derived by smoothing, with a cubic smoothing spline, the naive estimate of the spectrum obtained by applying FFT techniques to the raw data. By means of digital computer simulated results, a comparison is made between the features of the present approach and those of more classical techniques of spectral estimation.
Defigueiredo, R. J. P.↗
Power spectral density estimation by spline smoothing in the frequency domain.
An approach, based on a global averaging procedure, is presented for estimating the power spectrum of a second order stationary zero-mean ergodic stochastic process from a finite length record. This estimate is derived by smoothing, with a cubic smoothing spline, the naive estimate of the spectrum obtained by applying Fast Fourier Transform techniques to the raw data. By means of digital computer simulated results, a comparison is made between the features of the present approach and those of more classical techniques of spectral estimation.-
De Figueiredo, R. J. P.↗
Bounding filter - A simple solution to lack of exact a priori statistics.
Wiener and Kalman-Bucy estimation problems assume that models describing the signal and noise stochastic processes are exactly known. When this modeling information, i.e., the signal and noise spectral densities for Wiener filter and the signal and noise dynamic system and disturbing noise representations for Kalman-Bucy filtering, is inexactly known, then the filter's performance is suboptimal and may even exhibit apparent divergence. In this paper a system is designed whereby the actual estimation error covariance is bounded by the covariance calculated by the estimator. Therefore, the estimator obtains a bound on the actual error covariance which is not available, and also prevents its apparent divergence.
Nahi, N. E.↗
Statistical properties of two sine waves in Gaussian noise.
A detailed study is presented of some statistical properties of a stochastic process that consists of the sum of two sine waves of unknown relative phase and a normal process. Since none of the statistics investigated seem to yield a closed-form expression, all the derivations are cast in a form that is particularly suitable for machine computation. Specifically, results are presented for the probability density function (pdf) of the envelope and the instantaneous value, the moments of these distributions, and the relative cumulative density function (cdf).
Esposito, R.↗
Use of the Wigner representation in scattering problems
The basic equations of quantum scattering were translated into the Wigner representation, putting quantum mechanics in the form of a stochastic process in phase space, with real valued probability distributions and source functions. The interpretative picture associated with this representation is developed and stressed and results used in applications published elsewhere are derived. The form of the integral equation for scattering as well as its multiple scattering expansion in this representation are derived. Quantum corrections to classical propagators are briefly discussed. The basic approximation used in the Monte-Carlo method is derived in a fashion which allows for future refinement and which includes bound state production. Finally, as a simple illustration of some of the formalism, scattering is treated by a bound two body problem. Simple expressions for single and double scattering contributions to total and differential cross-sections as well as for all necessary shadow corrections are obtained.
Bemler, E. A.↗
A non-gaussian model of continuous atmospheric turbulence for use in aircraft design
A non-Gaussian model of atmospheric turbulence is presented and analyzed. The model is restricted to the regions of the atmosphere where the turbulence is steady or continuous, and the assumptions of homogeneity and stationarity are justified. Also spatial distribution of turbulence is neglected, so the model consists of three independent, stationary stochastic processes which represent the vertical, lateral, and longitudinal gust components. The non-Gaussian and Gaussian models are compared with experimental data, and it is shown that the Gaussian model underestimates the number of high velocity gusts which occur in the atmosphere, while the non-Gaussian model can be adjusted to match the observed high velocity gusts more satisfactorily. Application of the proposed model to aircraft response is investigated, with particular attention to the response power spectral density, the probability distribution, and the level crossing frequency. A numerical example is presented which illustrates the application of the non-Gaussian model to the study of an aircraft autopilot system. Listings and sample results of a number of computer programs used in working with the model are included.
Reeves, P. M.↗
On the role of dimensionality and sample size for unstructured and structured covariance matrix estimation
The experimental observation that a surprisingly small sample size vis-a-vis dimension is needed to achieve good signal-to-interference ratio (SIR) performance with an adaptive predetection filter is explained. The adaptive filter requires estimates as obtained by a recursive stochastic algorithm of the inverse of the filter input data covariance matrix. The SIR performance with sample size is compared for the situations where the covariance matrix estimates are of unstructured (generalized) form and of structured (finite Toeplitz) form; the latter case is consistent with weak stationarity of the input data stochastic process.
Morgera, S. D.↗
Status of dual control theory
Theoretical studies of decision making and stochastic processes are discussed. Several approaches are described for an improved performing control method. It is shown that control performance is highly dependent on the knowledge of the unknown parameters in the system.
Tse, E.↗
Optimal ride control for the Twin Otter, STOL aircraft
An aircraft with low wing loading, such as the deHavilland, Twin Otter, exhibits a relatively large acceleration sensitivity to wind gusts. These undesirable aircraft motions can be reduced using an automatic ride control system. In this paper, the techniques of quadratic optimal control theory are utilized to investigate the capabilities of such a ride control system. The effects of the wind gusts on the aircraft can be modeled by a vector stochastic process containing seven states. The impact of this disturbance model on the optimal control system structure is assessed and comparison is made to a system without gust feedback.
Holley, W. E.↗
Nonparametric algorithms for the search of signals
Two algorithms for the search of signals in noise are constructed. Two independent measurable properties of a discreet time-dependent stochastic process F are described. The functions A sub K and B sub K fully satisfy conditions for the application of a test based on Spearman's rank correlation coefficient. A statistic to which the one-sided signal test can be applied is constructed under sufficiently natural assumptions about the noise process. The constructed statistics are simplified. Processing results from calculations of statistics constructed for concrete processes are presented.
Myshenkova, T. S.↗
The analytical design of spectral measurements for multispectral remote sensor systems
The author has identified the following significant results. In order to choose a design which will be optimal for the largest class of remote sensing problems, a method was developed which attempted to represent the spectral response function from a scene as accurately as possible. The performance of the overall recognition system was studied relative to the accuracy of the spectral representation. The spectral representation was only one of a set of five interrelated parameter categories which also included the spatial representation parameter, the signal to noise ratio, ancillary data, and information classes. The spectral response functions observed from a stratum were modeled as a stochastic process with a Gaussian probability measure. The criterion for spectral representation was defined by the minimum expected mean-square error.
Wiersma, D. J.↗
The REH theory of protein and nucleic acid divergence - A retrospective update
The random evolutionary hits (REH) theory of evolutionary divergence, originally proposed in 1972, is restated with attention to certain aspects of the theory that have caused confusion. The theory assumes that natural selection and stochastic processes interact and that natural selection restricts those codon sites which may fix mutations. The predicted total number of fixed nucleotide replacements agrees with data for cytochrome c, a-hemoglobin, beta-hemoglobin, and myoglobin. The restatement analyzes the magnitude of possible sources of errors and simplifies calculational methodology by supplying polynomial expressions to replace tables and graphs.
Holmquist, R.↗