Rudolf E. Kálmán

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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(More)
The need to assess subtle, potentially exploitable changes in serial structure is paramount in the analysis of financial data. Herein, we demonstrate the utility of approximate entropy (ApEn), a model-independent measure of sequential irregularity, toward this goal, by several distinct applications. We consider both empirical data and models, including(More)
The need to assess the randomness of a single sequence, especially a finite sequence, is ubiquitous, yet is unaddressed by axiomatic probability theory. Here, we assess randomness via approximate entropy (ApEn), a computable measure of sequential irregularity, applicable to single sequences of both (even very short) finite and infinite length. We indicate(More)
The realization theory linear dynamical systems, previously developed over a field, are extended to a large class of commutative rings. The principal result is that the existence criterion for a finite realization extends without modification from a field to a Noetherian integral domain.
  • R E Kalman
  • Proceedings of the National Academy of Sciences…
  • 1969
A new algebraic criterion is given for a polynomial phi with complex coefficients to have all its zeros in a certain type of algebraic region T of the complex plane. In particular, T may be any circle or half plane. The criterion is effectively computable from the coefficients of the polynomial phi. The classical results of Hermite, Hurwitz, Lyapunov,(More)
A method is described for constructing a feedback control law which remains optimal for a class of systems with unknown parameters whose values may lie in given regions. The control depends only on the input and output, and there is no explicit dependence on the unknown parameters. In contrast to the usual adaptive sirategy, there is no identification or(More)