Z-type neural-dynamics for time-varying nonlinear optimization under a linear equality constraint with robot application

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:327

Article

Li, Jian¹  Mao, Mingzhi¹  Uhlig, Frank²  Zhang, Yunong¹ 

[1] Sun Yat Sen Univ, Sch Informat Sci & Technol, Guangzhou 510006, Guangdong, Peoples R China

[2] Auburn Univ, Dept Math & Stat, Auburn, AL 36849 USA

关键词: Z-type neural-dynamics;    Time-varying nonlinear optimization;    Linear equality constraint;    Four-instant finite difference formula;    Robot application;   

DOI  :  10.1016/j.cam.2017.06.017

来源: Elsevier

【 摘 要 】

Nonlinear optimization is widely important for science and engineering. Most research in optimization has dealt with static nonlinear optimization while little has been done on time-varying nonlinear optimization problems. These are generally more complicated and demanding. We study time-varying nonlinear optimizations with time-varying linear equality constraints and adapt Z-type neural-dynamics (ZTND) for solving such problems. Using a Lagrange multipliers approach we construct a continuous ZTND model for such time-varying optimizations. A new four-instant finite difference (FIFD) formula is proposed that helps us discretize the continuous ZTND model with high accuracy. We propose the FDZTND-K and FDZTND-U discrete models and compare their quality and the advantage of the FIFD formula with two standard Euler-discretization ZTND models, called EDZTND-K and EDZTND-U that achieve lower accuracy. Theoretical convergence of our continuous and discrete models is proved and our methods are tested in numerical experiments. For a real world, we apply the FDZTND-U model to robot motion planning and show its feasibility in practice. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

Free