Art Krener, Mar 2014

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Art Krener will be visiting Caltech on 3 Mar 2014 (Mon). IF you would like to meet with him, sign up below.

Schedule

  • 10:30 - Richard Murray, 109 Steele Lab
  • 11:00 - Seminar, 121 Annenberg
  • 12:00 - Lunch with Richard and John
  • 1:30 - Eric Wolff, 331 Annenberg
  • 2:15 - Matanya Horowitz, 335 Annenberg
  • 3:00 - Yilin Mo, 310 Annenberg
  • 3:45 - Done for the day

Abstract

Computational Issues in Nonlinear Control

Arthur J. Krener, Naval Postgraduate School
3 March 2014 - 11:00am PST, 121 Annenberg

Over the past several decades there has been tremendous progress in the development of nonlinear systems theory but implementation of these ideas have lagged behind because of the lack of effective computational tools. Frequently the nonlinear theory requires the solution of partial differential equations in continuous time and functional equations in discrete time. Algorithms for these have been developed but further work is needed to make them broadly and easily accessible. We believe that computational nonlinear control is in a similar stage of development that computational linear control was in around early 1980s. Then there was a well developed theory of linear control but computational tools lagged behind. Soon after comprehensive tools such as MATLAB and Matrix X were developed and put to great use in implementing the linear theory. Advancements in numerical methods together with the exponential increase in computational power has made it possible to solve complex nonlinear problems, many of which are closely related to control systems applications. Developing computational algorithms and software tools for such control systems are not only promising, but also necessary.

The three topics that we will focus on are the following.

  1. Numerical solution of Hamillton-Jacobi-Bellman and Dynamic Programming equations
  2. Numerical calculation of optimal trajectories
  3. Numerical calculation of invariant manifolds