Contributions to linear control theory

Contributions to time-varying Linear Control Systems

Contributions to the Theory of Optimal Control

THIS is one of the two ground-breaking papers by Kalman that appeared in 1960—with the other one (discussed next) being the filtering and prediction paper. This first paper, which deals with linear-quadratic feedback control, set the stage for what came to be known as LQR (Linear-Quadratic-Regulator) control, while the combination of the two papers formed the basis for LQG (Linear-Quadratic-Gau...

Contributions to Persistence Theory

Persistence theory discussed in this paper 1 is an application of algebraic topology (Morse Theory) to Data Analysis, precisely to qualitative understanding of point cloud data. Mathematically a point cloud data is a finite metric space of a very large cardinality. It can be geometrized as a filtration of simplicial complexes and the homology changes of these complexes provide qualitative infor...

Contributions to geomagnetic theory

Acknowledgements The number o f in d iv id u a ls and o rg an iz atio n s who c o n trib u te d to th e work d escrib ed in t h i s paper i s so la rg e th a t some must accep t the a u th o r's thanks w ithout s p e c ific mention h e re. He must, however, e s p e c ia lly thank Dr. S ta te U n iv ersity o f Iowa, f o r suggesting the to p ic d iscu ssed in th e second p a r t of th e paper, f...

Contributions to Metric Number Theory

The aim of this work is to investigate some arithmetical properties of real numbers, for example by considering sequences of the type ([bα]) , n = 1, 2, . . . where b ∈ N, α ∈ R, the terms of the sequences being in arithmetical progression, square-free, sums of two squares or primes. The results are most commonly proved for almost all α ∈ R or (α1, . . . , αm) ∈ R m (in the sense of Lebesgue me...