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Mathematical Problems in Engineering
Volume 2017, Article ID 6843614, 11 pages
https://doi.org/10.1155/2017/6843614
Research Article

Solving a Class of Nonlinear Inverse Problems Using a Feedback Control Approach

Department of Computer Science, San Diego State University, San Diego, CA 92128-7720, USA

Correspondence should be addressed to Mahmoud Tarokh; ude.usds.liam@hkoratm

Received 28 February 2017; Revised 8 April 2017; Accepted 10 April 2017; Published 28 May 2017

Academic Editor: J.-C. Cortés

Copyright © 2017 Mahmoud Tarokh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Inverse problems have applications in many branches of science and engineering. In this paper we propose a new approach to solving inverse problems which is based on using concepts from feedback control systems to determine the inverse of highly nonlinear, discontinuous, and ill-conditioned input-output relationships. The method uses elements from least squares solutions that are formed within a control loop. The stability and convergence of the inverse solution are established. Several examples demonstrate the applicability of the proposed method.