# Arthur J Krener

Web Page: http://www.math.ucdavis.edu/~krener/

Email: krener@math.ucdavis.edu

Office: MSB 3208

### Research

Arthur Krener is a mathematician whose research interests are in developing methods for the control and estimation of nonlinear dynamical systems and stochastic processes. In 1971 he received the PhD in Mathematics from the University of California, Berkeley and joined the faculty of the University of California, Davis. He retired from UCD in 2006 as a Distinguished Professor of Mathematics and he currently is a Distinguished Visiting Professor at the Naval Postgraduate School. He has also held visiting positions at Harvard University, Imperial College, NASA Ames Research Center, the University of California, Berkeley, the University of Paris, the University of Maryland, the University of Padua and North Carolina State University. His research has been continuously funded since 1975 by NSF, NASA, AFOSR and ONR.

He is a Fellow of the American Mathematical Association, a Fellow of the Society for Industrial and Applied Mathematics, a Life Fellow of the Institute of Electrical and Electronics Engineers and a Fellow of the International Federation for Automatic Control. Krener has held a variety of administrative posts, including Chair of the Department of Mathematics, UC Davis, member of the Committee on Academic Personnel, UC Davis and founding Chair of the SIAM Activity Group on Control and Systems Theory. He has given numerous invited addresses at professional meetings. He has organized several major conferences including the SIAM Conferences on Control and its Applications in 1989 and 2007 in San Francisco and the IFAC NOLCOS at Lake Tahoe in 1996 and In Monterey, 2016.

Krener has been a leader in the development of software tools for nonlinear control. His Nonlinear Systems Toolbox is a suite of MATLAB routines that implement a variety of the latest methods of nonlinear control. He was also co-PI on an AFOSR sponsored multicampus research project to control surge, stall and flutter in compressors and aeroengines.

Krener in collaboration with Wei Kang discovered that there is a theory of bifurcations for control systems. Using a newly developed theory of normal forms for control systems, Kang, Krener and colleagues have been able to classify the low codimension control bifurcations and in some cases develop truly nonlinear feedbacks to stabilize them.

In 2002 Krener showed that, under suitable conditions, the extended Kalman filter (the most widely used nonlinear estimator) is locally convergent. He also showed that under the same conditions the minimum energy estimator is globally convergent.

More recently he has developed methods for reduction of high dimensional models of control systems and methods for the numerical solution of Hamilton Jacobi Bellman PDEs. He has also studied the observability of simple two dimensional flows under Eulerian and Lagrangian observations .

### Honors and Awards

- 2002, John Simon Guggenheim Fellowship
- 2004, Statistical and Applied Mathematical Sciences Institute University Fellow
- 2004, W. T. and Idalia Reid Prize from SIAM “for fundamental contributions to the control and estimation of nonlinear dynamical systems and stochastic processes”
- 2006, IEEE Control System Society Bode Prize Lecture “for fundamental contributions to the foundations of geometric nonlinear control theory”
- 2010, Certificate of Excellent Achievements from the IFAC Techical Commttee on Nonlinear Control
- October 2002, Symposium on New Trends in Nonlinear Dynamics and Control and Their Applications was held at the Naval Postgraduate School, in conjunction with his 60th birthday
- 2012, Richard Bellman Control Heritage Award from the American Automatic Control Council
- 2016, Field Award in Control Systems from Institute of Electrical and Electronic Engineers

### Recent Publications

For a more comprehensive list of Professor Krener's publications as well as the publications themselves, visit his web page.

2018 Krener, A. J., Minimum Energy Estimation Applied to the Lorenz Attaractor in Numerical Methods for Optimal Control Problems, M. Falcone, R. Ferreti, L. Grune, W. McEneaney Springer Verlag, pages 165-182.

2018 Krener, A. J., Adaptive Horizon Model Predictive Control, in the Proceedings of the IFAC Conference on Modeling, Identification and Control of Nonlinear Systems, Guadalajara, Mexico

2018 Krener, A. J., Adaptive Horizon Model Predictive Regulation, in the Proceedings of the IFAC Conference on Nonlinear Model Predictive Control, Madison, Wisconsin.

2019 Krener, A. J., Adaptive Horizon Model Predictive Control and Al’brekht’s Method, Encylopedia of Systems and Control, Springer-Verlag, London.

2019 Krener, A. J., Stochastic HJB Equations and Regular Singular Points, in Modeling, Stochastic Control, Optimization, and Applications, G. Yin and Q. Zhang, eds., IMA Volumes in Mathematics and its Applications, Springe Nature, Switzerland, pages 351-368.

2019 Krener, A.J., Series Solution of Discrete Time Stochastic Optimal Control Problems, arXiv : submit/2607143 [math.OC]

2020 Krener, A. J., Series Solution of Stochastic Dynamic Programming Equations, Proceeding of the IFAC World Congress, Berlin.

*Last updated: 2020-07-14*