A Numberical Algorithm to Solve a Class of Multi-Point Boundary Value Problems

This note presents a numerical algorithm to solve a class of multi-point boundary value problems (MBVPs). Compared to conventional multiple shooting, the proposed method uses less parameters to exploit advantages of single shooting approaches. Unknown parameters are updated by a two-step algorithm which improves the convergence of parameters over existing one-step algorithm. The main idea of the two-step algorithm is to decouple the effects on boundary conditions between two sets of parameters: state and costate, and switch times. The proposed algorithm can compute the solution of a class of MBVPs faster than various existing methods. An application example illustrates the effects of the algorithm. Chinese Control Conference (CCC) This work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All rights reserved. Copyright c ©Mitsubishi Electric Research Laboratories, Inc., 2013 201 Broadway, Cambridge, Massachusetts 02139