By Topic

An approach to parametric nonlinear least square optimization and application to task-level learning control

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$33 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

1 Author(s)
D. Gorinevsky ; Fac. of Appl. Sci. & Eng., Toronto Univ., Ont., Canada

This paper considers a parametric nonlinear least square (NLS) optimization problem. Unlike a classical NLS problem statement, we assume that a nonlinear optimized system depends on two arguments: an input vector and a parameter vector. The input vector can be modified to optimize the system, while the parameter vector changes from one optimization iteration to another and is not controlled. The optimization process goal is to find a dependence of the optimal input vector on the parameter vector, where the optimal input vector minimizes a quadratic performance index. The paper proposes an extension of the Levenberg-Marquardt algorithm for a numerical solution of the formulated problem. The proposed algorithm approximates the nonlinear system in a vicinity of the optimum by expanding it into a series of parameter vector functions, affine in the input vector. In particular, a radial basis function network expansion is considered. The convergence proof for the algorithm is presented. The proposed approach is applied to task-level learning control of a two-link flexible arm. Each evaluation of the system in the optimization process means completing a controlled motion of the arm

Published in:

IEEE Transactions on Automatic Control  (Volume:42 ,  Issue: 7 )