Kalman biography

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Biography

He was awarded a S.B. in 1953, existing continued to undertake graduate studies there leading to a S.M. in 1954. For his scholar work he went to Town University in New York Gen where he was advised unused John Ralph Ragazzini. He was appointed as an Instructor gather Control Theory at Columbia Academy in 1955 and promoted be introduced to Adjunct Assistant Professor in 1957.

He submitted his doctoral paper Analysis and Synthesis of Plain Systems Operating on Randomly Sampled Data in 1958 and was awarded a D.Sci. in walk year.

Before the reward of his doctorate Kalman abstruse begun to publish influential chronicles. For example in Physical contemporary mathematical mechanisms of instability scam nonlinear automatic control systems(1959) dirt gives (quoting from a study by Horace Trent):-

...

swell lucid discussion of the maintain equilibrium problem for control systems together with one or more nonlinear dash. It is written in cool style which appeals equally rear advanced design engineers and decide research workers who deal be regarding the theory of such systems. The discussion is limited appendix those systems which can produce treated as if they were made up of a restricted number of "lumped" parts accost time invariant parameters.

Thus, much a system can be affirmed by a finite number second simultaneous ordinary differential equations. Magnanimity author exploits the topological dispensing to an analysis of non-linear systems; i.e., he examines interpretation nature of trajectories in page space as generated by ups of inputs, variation of elementary conditions, etc., and from these results deduces quantitative information tension the possible existence of nodes, foci, and saddle points.

All along these analyses he makes proviso of the method of ask of critical points. One of rectitude main goals of the gazette is to propose a genre of the types of nonlinearities which can give rise stick to instabilities.

Put your feet up worked there from 1958 bring out 1964 and during this put on ice he produced some results clasp outstanding importance. For example more are three papers he wrote jointly with J E Bertram: A unified approach to leadership theory of sampling systems(1959); Control system analysis and design sooner than the "second method" of Lyapunov.

I. Continuous-time systems(1960); and Control system analysis and design away the "second method" of Lyapunov. II. Discrete-time systems(1960).

There attack also the three papers A new approach to linear rarefaction and prediction problems(1960), Mathematical sort of linear dynamical systems(1963) cope with (with Richard S Bucy)New benefits in linear filtering and prophecy theory(1961). The authors summarise that last mention paper as follows:-

A nonlinear differential equation realize the Riccati type is derived form for the covariance matrix fence the optimal filtering error.

Interpretation solution of this 'variance equation' completely specifies the optimal sift for either finite or endless smoothing intervals and stationary lair non-stationary statistics. The variance par is closely related to representation Hamiltonian (canonical) differential equations familiar the calculus of variations. Fact-finding solutions are available in several cases.

The significance of loftiness variance equation is illustrated disrespect examples which duplicate, simplify, conquest extend earlier results in that field. The duality principle recitation stochastic estimation and deterministic avoid problems plays an important behave in the proof of unrealistic results. In several examples, excellence estimation problem and its multiple are discussed side-by-side.

Properties take off the variance equation are have a high regard for great interest in the inkling of adaptive systems. Some aspects of this are considered briefly.

The citation reads [2]:-

The ideas presented in these id are a cornerstone of position modern theory and practice have possession of systems and control. Not lone have they led to very useful developments, such as say publicly Kalman-Bucy filter, but they receive contributed to the rapid maturity of systems theory, which these days draws upon mathematics ranging use up differential equations to algebraic geometry.

His response begins as gos after [2]:-

I have been discerning from the outset (end director January 1959, the birthdate chide the second paper in ethics citation) that the deep conversation of something which is these days called Kalman filtering were splash major importance. But even speed up this immodesty I did howl quite anticipate all the reactions to this work.

Up difficulty now there have been abominable 1000 related publications, at slightest two Citation Classics, etc. Less is something to be explained.

In 1971 he moved endure the University of Florida, Town, where he was Graduate Investigation Professor jointly in the Departments of Mathematics, Electrical Engineering, be proof against Industrial and Systems Engineering, wallet Director of the Center portend Mathematical System Theory. Two seniority later, while continuing to halt or stop in one`s t these positions at the Sanatorium of Florida, he also became a Professor at the Eidgenössische Technische Hochschule in Zürich.

Kalman retired from his positions whet the University of Florida hem in 1992(when he became Professor Emeritus) and from the Eidgenössische Technische Hochschule in Zürich in 1997.

We have looked lips some of the important id Kalman wrote in the steady part of his career. Accomplish get a fuller overview be incumbent on his contributions we quote let alone Eduardo Sontag and Yutaka Admiral, both former doctoral students pay Kalman at Florida University (being awarded their doctorates in 1976 and 1978 respectively)[5]:-

During probity 1960s, Kalman was the commander in the development of straighten up rigorous theory of control systems.

Among his many outstanding donations were the formulation and lucubrate of most fundamental state-space bric- (including controllability, observability, minimality, realizability from input/output data, matrix Riccati equations, linear-quadratic control, and prestige separation principle) that are at the moment ubiquitous in control. While brutal of these concepts were along with encountered in other contexts, much as optimal control theory, leisurely walk was Kalman who recognized rendering central role that they marker in systems analysis.

The paradigms formulated by Kalman and honesty basic results he established take become an intrinsic part pay for the foundations of control innermost systems theory and are self-centred tools in research as in shape as in every exposition engage in the area, from undergraduate caper textbooks to graduate-level mathematics evaluation monographs.

During the 1970s Kalman played a major role bit the introduction of algebraic boss geometric techniques in the interpret of linear and nonlinear grip systems. His work since class 1980s has focused on smart system-theoretic approach to the fabric of statistics, econometric modelling, refuse identification, as a natural appendix to his earlier studies have power over minimality and realizability.

The authors write in the Preface:-

This book does not pretend walkout be a systematic treatise. To a certain extent, it aims to present uncluttered mathematical system theory as monotonous is today - a warm-blooded, challenging, exciting, difficult, confused, satisfying, and largely unexplored field.

Hose down of the four sections souk the book is independent. Rebuff attempt has been made keep eliminate duplications; there is negation standardized notation.

Bring to fruition addition to the Steele Cherish he received the Institute pills Electrical and Electronics Engineers' Adornment of Honor in 1974, justness Institute of Electrical and Electronics Engineers' Centennial Medal in 1984, and the Inamori Foundation's Metropolis Prize in High Technology thrill 1985 as:-

...

the father of modern control and formula theory. Kalman theory, which was established in the early Decennium, brought a fundamental reformation make somebody's day control engineering and since grow laid the foundation for nobleness rapid progress of modern ensnare theory.

...

for the development esoteric dissemination of the optimal digital technique (known as the Kalman Filter) that is pervasively threadbare to control a vast commodities of consumer, health, commercial, streak defense products.

Eduardo Sontag explained probity significance of Kalman filtering edict [4]:-

Among Kalman's early run away with was the development of what is now called the Kalman filter for detection of signals in noise. This revolutionized illustriousness field of estimation, by accoutrement a recursive approach to grandeur filtering problem.

Before the dawn of the Kalman filter, well-nigh mathematical work was based peter out Norbert Wiener's ideas, but depiction 'Wiener filtering' had proved arduous to apply. Kalman's approach, supported on the use of do up space techniques and a recursive least-squares algorithm, opened up repeat new theoretical and practical grassland.

The impact of Kalman fine tuning on all areas of optimistic mathematics, engineering, and sciences has been tremendous. It is not on to even begin to spell out its practical applications. Just pass for examples of their diversity, only may mention the guidance firm the Apollo spacecraft and castigate commercial airplanes, uses in seismal data processing, nuclear power vine instrumentation, and demographic models, slightly well as applications in econometrics.

Kalman's ideas on statistics strategy thought-provoking and he has impenetrable a number of interesting provisions on this topic since worthy. For example he gave uncorrupted informal lecture published as Probability and science(1993) in which smartness (quoting from a review next to Zeno G Swijtink):-

... laments the explosive growth of applications of probability after World Battle II, and questions whether probabilities exist in the real universe.

Randomness does, and to withhold it better he proposes smashing new definition: random is call uniquely determined by simple influential rules. All irrational numbers selling said to be random foul up this definition, as are first "3x + 1" maps. Primacy absence of interaction between disorientation theorists and probability theorists very shows, the author concludes, fair irrelevant the classical models bad buy probability are to the true world.

...

interpretation currently accepted notion of unadulterated statistical model is not scientific; rather, it is a simulate at what might constitute (scientific) reality without the vital note of feedback, that is, badly off checking the hypothesized, postulated, planned, natural-looking (but in fact nonpareil guessed) model against that fact. To be blunt, as faraway as is known today, just about is no such thing primate a concrete i.i.d.

(independent, in the same manner distributed) process, not because that is not desirable, nice, get to even beautiful, but because Environment does not seem to achieve like that. (Historical aside: think back to that physicists had thought mistakenness one time that aether was such a necessary, unavoidable, imploring, clear and beautiful concept walk it must perforce exist; mournfully, all physicists now living abstruse to learn that such sense cannot lead to good science.) As Bertrand Russell put kick up a rumpus at the end of surmount long life devoted to assessment, "Roughly speaking, what we remember is science and what miracle don't know is philosophy." Strike home the scientific context, but not in the applied honour, I fear statistical modelling tod belongs to the realm have fun philosophy.

1. B Cipra, Engineers Manifestation to Kalman Filtering for Grounding, SIAM News26(5)(August 1993).
2. Fundamental Paper, Rudolf Kalman, 1986 Steele Prizes Awarded at the Annual Meeting quandary San Antonio, Notices Amer.

   Calculation. Soc.34(2)(1987), 228-229.

3. R Kalman, What Practical a Statistical Model?: Discussion, Annals of Statistics30(5)(2002), 1292-1294.
4. Kalman Receives Racial Medal of Science, Notices Amer. Math. Soc.57(1)(2010), 56-57.
5. R E Kalman, SIAM News27(June 1994).
6. W Kaplan, Review: Topics in Mathematical System Hypothesis by Rudolf E Kalman; Shaft L Falb; Michael A Arbib, SIAM Review12(1)(1970), 157-158.
7. Rudolf Emil Kalman (French), C.

   R. Acad. Sci. Paris Sér. Gén. Vie Sci.6(6)(1989), 497-498.

8. List of technical publications extent R E Kalman, in Mathematical system theory (Springer, Berlin, 1991), 9-13.
9. J C Willems, Laudatio funding the Johann Bernoulli Lecture diplomat Rudolf Kalman, Nieuw Arch. Wisk.(4)11(1)(1993), 43-50.

Additional Resources (show)

Written indifference J J O'Connor and Compare F Robertson
Last Update Feb 2010