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Results for “Grassmannian”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS1982

Global differential geometry: An introduction for control engineers

The basic concepts and terminology of modern global differential geometry are discussed as an introduction to the Lie theory of differential equations and to the role of Grassmannians in control systems analysis. To reach these topics, the fundamental notions of manifolds, tangent spaces, vector fields, and Lie algebras are discussed and exemplified. An appendix reviews such concepts needed for vector calculus as open and closed sets, compactness, continuity, and derivative. Although the content is mathematical, this is not a mathematical treatise but rather a text for engineers to understand geometric and nonlinear control.

Doolin, 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.↗