Arthur James Krener (born October 8, 1942) is an American mathematician. He is a distinguished visiting professor in the department of applied mathematics at the

Naval Postgraduate School The Naval Postgraduate School (NPS) is a public graduate school operated by the United States Navy and located in Monterey, California. It offers master’s and doctoral degrees in more than 70 fields of study to the U.S. Armed Forces, DOD ci ...

. He has made contributions in the areas of

control theory Control theory is a field of mathematics that deals with the control of dynamical systems in engineered processes and machines. The objective is to develop a model or algorithm governing the application of system inputs to drive the system to a ...

nonlinear control Nonlinear control theory is the area of control theory which deals with systems that are nonlinear, time-variant, or both. Control theory is an interdisciplinary branch of engineering and mathematics that is concerned with the behavior of d ...

, and

stochastic processes In probability theory and related fields, a stochastic () or random process is a mathematical object usually defined as a family of random variables. Stochastic processes are widely used as mathematical models of systems and phenomena that a ...

Biography

He was born in

Brooklyn, New York Brooklyn () is a borough of New York City, coextensive with Kings County, in the U.S. state of New York. Kings County is the most populous county in the State of New York, and the second-most densely populated county in the United States, behi ...

, on October 8, 1942. He received BS in mathematics (1964) from

College of the Holy Cross The College of the Holy Cross is a private, Jesuit liberal arts college in Worcester, Massachusetts, about 40 miles (64 km) west of Boston. Founded in 1843, Holy Cross is the oldest Catholic college in New England and one of the olde ...

and an MA (1967) and PhD (1971), both in mathematics, from the

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...

. He was a professor of mathematics at the

University of California, Davis The University of California, Davis (UC Davis, UCD, or Davis) is a public land-grant research university near Davis, California. Named a Public Ivy, it is the northernmost of the ten campuses of the University of California system. The inst ...

for 35 years. He retired from Davis as a distinguished professor in 2006 and joined the department of applied mathematics,

at that time. His research interests are in developing methods for the control and estimation of nonlinear dynamical systems and stochastic processes. In 1988 he founded the SIAM Activity Group on Control and Systems Theory and was its first chair. He was again chair of the SIAG CST in 2005–07. In 2012, he received the Richard E. Bellman Control Heritage Award from the AACC. The citation reads "For contributions to the control and estimation of nonlinear systems." In 2016, he received the

IEEE Control Systems Award The IEEE Control Systems Award is a technical field award given to an individual by the Institute of Electrical and Electronics Engineers (IEEE) "for outstanding contributions to control systems engineering, science or technology". It is an IEEE- ...

for "contributions to the analysis, control, and estimation of nonlinear control systems."

Work

In his PhD dissertation, Krener showed that the

Lie bracket In mathematics, a Lie algebra (pronounced ) is a vector space \mathfrak g together with an operation called the Lie bracket, an alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow \mathfrak g, that satisfies the Jacobi identi ...

played an important role in nonlinear controllability by proving a time directed version of Chow's theorem. Several years later with

Hermann Hermann or Herrmann may refer to: * Hermann (name), list of people with this name * Arminius, chieftain of the Germanic Cherusci tribe in the 1st century, known as Hermann in the German language * Éditions Hermann, French publisher * Hermann, M ...

, he gave the definitive treatment of controllability and observability for nonlinear systems. This work was later cited by the

IEEE Control Systems Society The Institute of Electrical and Electronics Engineers (IEEE) is a 501(c)(3) professional association for electronic engineering and electrical engineering (and associated disciplines) with its corporate office in New York City and its operati ...

as one of Twenty Five Seminal Papers in Control, published in the twentieth century, which have made a major impact on the field of control. With Isidori, Gori-Giorgi and Monaco, he gave conditions for the existence and construction of decoupling and noninteracting control laws for nonlinear systems. This paper won the George S. Axelby Outstanding Paper Award from IEEE Transactions on Automatic Control and Krener received the Medal of the University of Rome for his contributions. It also led to the concept of the zero of a nonlinear system, which was subsequently developed by Byrnes and Isidori and extended to the

backstepping In control theory, backstepping is a technique developed circa 1990 by Petar V. Kokotovic and others for designing stabilizing controls for a special class of nonlinear dynamical systems. These systems are built from subsystems that radiate out f ...

technique of control by Kokotovic, Krstic and many others.

Awards

, IEEE, 2016. * Richard E. Bellman Control Heritage Award, AACC, 2012. * IFAC Certificate of Excellent Achievement, 2010. *

IEEE The Institute of Electrical and Electronics Engineers (IEEE) is a 501(c)(3) professional association for electronic engineering and electrical engineering (and associated disciplines) with its corporate office in New York City and its operati ...

Hendrik W. Bode Lecture Prize, 2006 *W.T. and Idalia Reid Prize in Mathematics,

SIAM Thailand ( ), historically known as Siam () and officially the Kingdom of Thailand, is a country in Southeast Asia, located at the centre of the Indochinese Peninsula, spanning , with a population of almost 70 million. The country is bo ...

, 2004. *

Guggenheim Fellowship Guggenheim Fellowships are grants that have been awarded annually since by the John Simon Guggenheim Memorial Foundation to those "who have demonstrated exceptional capacity for productive scholarship or exceptional creative ability in the ar ...

2001 *Fellow of the AMS, 2014 *Fellow of

, inaugural class of 2009 *Fellow of IFAC *Life Fellow of the

, 1990

References

External links

* {{DEFAULTSORT:Krener, Arthur 1942 births Living people Control theorists Richard E. Bellman Control Heritage Award recipients Fellows of the American Mathematical Society Educators from Brooklyn University of California, Berkeley alumni College of the Holy Cross alumni

Biography

Work

Awards

See also

References

External links