Title :
An algorithm for on-line parametric nonlinear least square optimization
Author :
Gorinevsky, Dimitry
Author_Institution :
Robotics & Autom. Lab., Toronto Univ., Ont., Canada
Abstract :
This paper considers a parametric nonlinear least square (NLS) optimization problem. In extension of a classical NLS problem statement, it is assumed that the 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 numerical solution of the formulated problem. The proposed algorithm approximates the nonlinear system by an expansion into a series of the 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
Keywords :
convergence of numerical methods; feedforward neural nets; iterative methods; least squares approximations; nonlinear control systems; optimisation; performance index; Levenberg-Marquardt algorithm; convergence proof; nonlinear optimized system; online parametric nonlinear least square optimization; optimal input vector; optimization iteration; parameter vector; quadratic performance index; radial basis function network expansion; Control systems; Ear; Laboratories; Least squares approximation; Least squares methods; Nonlinear systems; Optimal control; Performance analysis; Radial basis function networks; Robotics and automation;
Conference_Titel :
Decision and Control, 1994., Proceedings of the 33rd IEEE Conference on
Conference_Location :
Lake Buena Vista, FL
Print_ISBN :
0-7803-1968-0
DOI :
10.1109/CDC.1994.411491