Case studies on the application of the stable manifold approach for nonlinear optimal control design |
| |
| Authors: | Noboru Sakamoto |
| |
| Affiliation: | 1. Department of Electrical Engineering, Faculty of Science and Technology, Tokyo University of Science, Yamazaki 2641, Noda, Japan;2. Interdisciplinary Faculty of Science and Engineering, Shimane University, 1060 Nishikawatsu, Matsue, Japan;3. Ritsumeikan Global Innovation Research Organization (R-GIRO), Ritsumeikan University, 1-1-1 Noji-higashi, Kusatsu, Shiga, Japan;1. CESAME, Université Catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium;2. Department of Chemical Engineering, Queen’s University, Kingston, ON, Canada, K7L 3N6;1. School of Aerospace, Tsinghua University, Beijing 100084, China;2. Science and Technology on Aerospace Flight Dynamics Laboratory, Beijing 100094, China;3. Beijing Aerospace Control Center, Beijing 100094, China;1. Key Laboratory of Measurement and Control of Complex Systems of Engineering, Ministry of Education, Southeast University, Nanjing, Jiangsu 210096, China;2. School of Automation, Southeast University, Nanjing, Jiangsu, 210096, China |
| |
| Abstract: | This paper presents application results of a recently developed method for approximately solving the Hamilton–Jacobi equation in nonlinear control theory. The method is based on stable manifold theory and consists of a successive approximation algorithm which is suitable for computer calculations. Numerical approach for this algorithm is advantageous in that the computational complexity does not increase with respect to the accuracy of approximation and non-analytic nonlinearities such as saturation can be handled. First, the stable manifold approach for approximately solving the Hamilton–Jacobi equation is reviewed from the computational viewpoint and next, the detailed applications are reported for the problems such as swing up and stabilization of a 2-dimensional inverted pendulum (simulation), stabilization of systems with input saturation (simulation) and a (sub)optimal servo system design for magnetic levitation system (experiment). |
| |
| Keywords: | |
| 本文献已被 ScienceDirect 等数据库收录！ |
|
