Minimum Energy Estimation Applied to the Lorenz Attractor

Speaker: Arthur J. Krener
Affiliation: Naval Postgraduate School

Abstract:

Minimum Energy Estimation is a way of filtering the state of a   nonlinear system from partial and inexact measurements. It is a generalization of Gauss’ method of least squares.  Its application to filtering of control systems goes back at least to Mortenson who called it Maximum Likelyhood Estimation.  For linear, Gaussian systems it reduces to maximum likelihood estimation (aka Kalman Filtering) but this is not true for nonlinear systems.  We prefer the name Minimum Energy Estimation (MEE) that was introduced by Hijab.   Both Mortenson and Hijab dealt with systems in continuous time, we extend their methods to discrete time systems and show how Taylor polynomial techniques can lessen the computational burden.

The degree one version is equivalent to the Extended Kalman Filter in Information form.  We apply this and the degree three version to problem of estimating the state of the three dimensional Lorenz Attractor from a one dimensional measurement.

Biography:  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 member of the American Mathematical Association, a Fellow of the Society for Industrial and Applied Mathematics and a Life Fellow of the Institute of Electrical and Electronics Engineers. 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 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.

For more information, contact Prof. Paulo Tabuada (tabuada@ucla.edu)

Date/Time:
Date(s) - Feb 23, 2018
2:00 pm - 3:30 pm

Location:
E-IV Tesla Room #53-125
420 Westwood Plaza - 5th Flr., Los Angeles CA 90095