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Hermann, R.

Publications and source records attributed to Hermann, R..

At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1997

Evidence for Highly Inhomogeneous mm-Wave Sources During the Impulsive Flare of May 9, 1991

In this paper multiwavelength observations of an impulsive flare of May 9, 1991 are presented. This event was observed with the 48 GHz multibeam focal array used at the Itapetinga radio telescope, the microwave patrol telescopes at Bem and the BATSE high time resolution hard X-ray spectrometer on board CGRO. While spatially unresolved low sensitivity observations show two major impulsive peaks, the mm-wave observations with the ability of spatially high resolved tracking of the emission centroids suggest a primarily bipolar source configuration. For the first time two mm-wave sources with a spacing below the HPBW could be separated with the multibeam technique. The general features of the observations are explained as emission of partially trapped electrons. Furthermore we present evidence for highly inhomogeneous substructures within one of the two mm-wave sources for which the positional scatter of the emission center, within 2s, is less than 2".

Hermann, R.↗
NASA NTRS1987

Geometric foundations of the theory of feedback equivalence

A description of feedback control is presented within the context of differential equations, differential geometry, and Lie theory. Work related to the integration of differential geometry with the control techniques of feedback linearization is summarized. Particular attention is given to the application of the theory of vector field systems. Feedback invariants for control systems in state space form are also addressed.

Hermann, R.↗
NASA NTRS1983

Pfaffian systems and feedback linearization/obstructions

The concept of Cartan-Vessiot filtered Lie algebra/module is defined in terms of previous feedback linearizations constructed through canonical forms of Pfaffian systems associated with nonlinear systems. Nonlinearization/Cartan-Vessiot algebras are regarded as deformations of linear ones. It is shown how certain problems of interest in nonlinear system theory translate over to algebraic problems involving this sort of algebraic structure.

Hermann, R.↗
NASA NTRS1980

Periodic solutions of the Riccati equation

It is shown that the Riccati equations of control theory are generically Morse-Smale. The existence of periodic solutions is explicitly demonstrated. The principal contribution here is thought to be the presentation of a mathematical structure in which to study the Riccati equation. Mathematical structures already in the literature are systematically exploited. It is also shown that most problems of the Riccati equation can be reduced to problems in linear algebra. A framework is developed for studying the Riccati equation, and the proof that the Morse-Smale conditions are satisfied is outlined.

Hermann, R.↗
NASA NTRS1979

System theory as applied differential geometry

The invariants of input-output systems under the action of the feedback group was examined. The approach used the theory of Lie groups and concepts of modern differential geometry, and illustrated how the latter provides a basis for the discussion of the analytic structure of systems. Finite dimensional linear systems in a single independent variable are considered. Lessons of more general situations (e.g., distributed parameter and multidimensional systems) which are increasingly encountered as technology advances are presented.

Hermann, R.↗
NASA NTRS1979

Time-varying linear systems and the theory of non-linear waves

The isospectral deformation of a Sturm-Liouville equation is extended to general linear time-varying systems and a method is described for determining the resulting nonlinear partial differential equations. Consideration is given to (1) isospectral deformation of I/O systems with boundary value conditions and (2) the spectral vector bundles attached to linear time-varying systems.

Hermann, R.↗
NASA NTRS1978

Assess II - A simulated mission of Spacelab

For Assess II, the Spacelab mission simulation conducted in mid-1977, four payload specialists aboard a Convair 990 research aircraft performed six American and six European experiments during nine research flights each of six hours duration in order to evaluate the compatibility of training and experimental design. Mission organization and some initial data from the European experiments are reported. The experiments, conducted over the western U.S., involved infrared astronomy, solar brightness temperature, lidar, airglow TV, and a medical experiment for which physiological parameters were monitored. Conclusions concerning general principles of experiment design are discussed.

Wegmann, H. M.↗
NASA NTRS1977

Linear systems with structure group and their feedback invariants

A general method described by Hermann and Martin (1976) for the study of the feedback invariants of linear systems is considered. It is shown that this method, which makes use of ideas of topology and algebraic geometry, is very useful in the investigation of feedback problems for which the classical methods are not suitable. The transfer function as a curve in the Grassmanian is examined. The general concepts studied in the context of specific systems and applications are organized in terms of the theory of Lie groups and algebraic geometry. Attention is given to linear systems which have a structure group, linear mechanical systems, and feedback invariants. The investigation shows that Lie group techniques are powerful and useful tools for analysis of the feedback structure of linear systems.

Martin, C.↗
NASA NTRS1977

Lie theoretic aspects of the Riccati equation

Various features of the application of Lie theory to matrix Riccati equations, of basic importance in control and system theories, are discussed. Particular consideration is given to centralizer foliation, the Cartan decomposition, matrix Riccati equations as Lie systems on Grassmanians, local analysis near a zero point of a vector field, linearization in homogeneous space, the tangent bundle in terms of partitioned matrices, and stability properties of fixed points of Riccati vector fields.

Hermann, R.↗
NASA NTRS1976

Pseudopotentials of Estabrook and Wahlquist, the geometry of solitons, and the theory of connections

The prolongation structure of Wahlquist and Estabrook is interpreted as a connection. In this way, some geometric insight might be provided for the description of those nonlinear partial differential equations which admit soliton solutions. A new geometric property - linked to the existence of an SL(2,R) connection - is proved for the solutions of the Korteweg-de Vries equation.

Hermann, R.↗
NASA NTRS1976

A new application of algebraic geometry to systems theory

Following an introduction to algebraic geometry, the dominant morphism theorem is stated, and the application of this theorem to systems-theoretic problems, such as the feedback problem, is discussed. The Gaussian elimination method used for solving linear equations is shown to be an example of a dominant morphism.

Martin, C. F.↗