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All sourcesNASA NTRSDOE OSTI
NASA NTRS1976

Response of linear dynamic systems with random coefficients

Numerous models of physical systems contain parameters whose values are not known exactly. The physical and mathematical complexities arising in the prediction of the statistical behavior of such systems are discussed. Although the discussions are far from providing a satisfactory solution to such problems, they perhaps, by utilization of simple examples, will create a greater awareness of the statistical effect of random parameters.

Dickerson, J.↗
NASA NTRS1972

Fixed interval smoothing with discrete measurements.

Smoothing equations for a linear continuous dynamic system with linear discrete measurements, derived from the discrete results of Rauch, Tung, and Striebel (1965), (R-T-S), are used to extend, through recursive updating, the previously published results of Bryson and Frazier (1963), (B-F), and yield a modified Bryson and Frazier, (M-B-F), algorithm. A comparison of the (M-B-F) and (R-T-S) algorithms leads to the conclusion that the former is to be preferred because it entails less computation, less storage, and less instability. It is felt that the presented (M-B-F) smoothing algorithm is a practical mechanization and should be of value in smoothing discretely observed dynamic linear systems.

Bierman, G. J.↗
NASA NTRS1992

Non-linear dynamic compensation system

A non-linear dynamic compensation subsystem is added in the feedback loop of a high precision optical mirror positioning control system to smoothly alter the control system response bandwidth from a relatively wide response bandwidth optimized for speed of control system response to a bandwidth sufficiently narrow to reduce position errors resulting from the quantization noise inherent in the inductosyn used to measure mirror position. The non-linear dynamic compensation system includes a limiter for limiting the error signal within preselected limits, a compensator for modifying the limiter output to achieve the reduced bandwidth response, and an adder for combining the modified error signal with the difference between the limited and unlimited error signals. The adder output is applied to control system motor so that the system response is optimized for accuracy when the error signal is within the preselected limits, optimized for speed of response when the error signal is substantially beyond the preselected limits and smoothly varied therebetween as the error signal approaches the preselected limits.

Lin, Yu-Hwan↗
NASA NTRS1965

Contributions to linear system theory.

Linear dynamic systems governed by first-order linear differential equations in state variables, emphasizing time reversal and differential controllability

STATE EQUATION↗
NASA NTRS2006

Parameter and Structure Inference for Nonlinear Dynamical Systems

A great many systems can be modeled in the non-linear dynamical systems framework, as x = f(x) + xi(t), where f() is the potential function for the system, and xi is the excitation noise. Modeling the potential using a set of basis functions, we derive the posterior for the basis coefficients. A more challenging problem is to determine the set of basis functions that are required to model a particular system. We show that using the Bayesian Information Criteria (BIC) to rank models, and the beam search technique, that we can accurately determine the structure of simple non-linear dynamical system models, and the structure of the coupling between non-linear dynamical systems where the individual systems are known. This last case has important ecological applications.

Morris, Robin D.↗
NASA NTRS1972

A biased filter for linear discrete dynamic systems.

A recursive estimator, the ridge filter, was developed for the linear discrete dynamic estimation problem. Theorems were established to show that the ridge filter can be, on the average, closer to the expected value of the system state than the Kalman filter. On the other hand, Kalman filter, on the average, is closer to the instantaneous system state than the ridge filter. The ridge filter has been formulated in such a way that the computational features of the Kalman filter are preserved.

Chang, J. W.↗
NASA NTRS1985

On the design of pole modules for inverse systems

When a linear dynamical system admits more than one inverse, it is known that the pole module of any inverse must contain, either as a submodule or as a factor module, a module of fixed poles isomorphic to the zero module of the original system. Design of the pole module for such an inverse system is resolved by introducing a variable pole module for the inverse, by determining necessary and sufficient conditions for a desired module to be a variable pole module, and by studying the manner in which the fixed and variable modules assemble into the pole module of the inverse. If the fixed and variable pole spectra are disjoint, the pole module of the inverse system is a direct sum of the fixed- and variable-pole modules; if not, procedures for addressing the Jordan structure are presented.

Wyman, B. F.↗
NASA NTRS1988

An approach to simultaneous system design. II - Nonswitching gain and dynamic feedback compensation by algebraic geometric methods

This paper studies structured uncertainty problems in feedback system design, considers a compact parameterization of the space of linear dynamical systems and introduces 'base points' and 'critical points' as two algebraic-geometric objects that have significance in sensitivity and robustness studies, respectively. Using the Nevanlinna-Pick interpolation theory, the author obtains a necessary and sufficient condition for simultaneous stabilization of a structured one-parameter family of plants. A recent result due to Kharitonov, on the simultaneous stability of a parameterized family of polynomials, leads to a sufficiency condition for simultaneous stabilization of a structured multiparameter family of plants. Furthermore, the author considers 'simultaneous pole placement' of an r-tuple of plants as a means to arbitrarily tune the natural frequencies of a multimode linear dynamical system. The concept of 'nondegenerate' and 'twisted' r-tuples of plants is introduced as the pole placement problem is studied via Schubert enumerative geometry as an intersection problem on the associated Grassmannian. Various other design problems, viz., the strong stabilization problem and the dead beat control problem, are also considered.

Ghosh, Bijoy K.↗
NASA NTRS1980

System identification of large space structures

The paper deals with the problem of system identifiability for a linear dynamical system. Two theorems are given relating the sufficient condition of system identifiability for certain linear structures to the total number of inputs and outputs. The principle of least squares, that seeks the minimization of a cost function is employed to carry out the system identification process. To illustrate the concept of the paper, a structural model of a beam with point masses is examined. Parameter identification methods are studied and a random search technique is introduced.

Juang, J. N.↗
NASA NTRS1976

Linearization of dynamical systems using integrals of the motion

A method is presented which transforms certain nonlinear differential equations of dynamics into linear equations by introducing an independent variable and utilizing the integrals of motion. As examples of special interest, the linearizations of unperturbed and perturbed Keplerian motions are discussed.

Szebehely, V.↗