陳明新臺灣大學：機械工程學研究所游天佑Yu, Tien-YuTien-YuYu2007-11-282018-06-282007-11-282018-06-282004http://ntur.lib.ntu.edu.tw//handle/246246/61611在本篇論文中，我們要介紹一個離線最佳化控制及狀態估測應用於一般非線性系統.我們使用擾動方法發展出一套關於控制以及估測的演算法.當被線性化後的系統是一個線性時變系統時,我們可以使用線性系統理論去找到適當的控制及估測.而模擬出來的結果也可以顯示出我們提出的控制演算法確實可以找到最佳化的控制;狀態估測演算法也可以找到非線性系統之初始值.This thesis studies off-line optimal control and estimation of general nonlinear systems. We use the perturbation method to develop control and estimation alogrithms. Since the perturbed (linearized) system is linear time-varying, we can use linear system theory to solve its control and estimation problem. The simulation results show that the proposed control algorithm is able to find local optimal controls, and the estimation algorithm works satisfactorily to recover the initial state of the nonlinear system.Index of Contents Abstract-Chinese version I Abstract-English version II Introduction............................1 Chapter1. Motion Planning for Linear Systems.................................2 1.1 Motion planning for nonlinear systems ... 3 1.2 Optimal motion planning for nonlinear system ........................................... 8 1.3 Example……………………14 Chapter2. State Estimation .....15 2.1 Example ..................................... 20 References ...............................22 Figures...................................23 Figure I The flow chart of state transition control ........................................... 23 Figure II The flow chart of optimal control ..................................................... 24 Figure III The flow chart of state estimation ................................................... 25 Figure 1.3.1.1 End point error…………………………………………………….26 Figure 1.3.1.2 Minimum singular value of extended W.................................. 26 Figure 1.3.1.3 Minimum singular value of W ............................................... 27 Figure 1.3.1.4 The cost function .......... 27 Figure 1.3.1.5 The control u................ 28 Figure 1.3.1.6 Phase portraits .......... 28 Figure 1.3.1.7 End point error for different h .................... 29 Figure 1.3.1.8 Norm of du ............. 29 Figure 1.3.2.1 End point error…………………………………………………….30 Figure 1.3.2.2 Minimum singular value of extended W.................................. 30 Figure 1.3.2.3 Minimum singular value of W ............................................... 31 Figure 1.3.2.4 The cost function ....... 31 Figure 1.3.2.5 The control u............... 32 Figure 1.3.2.6 Phase portraits ....... 32 Figure 1.3.2.7 End point error for different h .................. 33 Figure 1.3.2.8 Norm of du ............33 Figure 2.1.1.1 The cost function ......34 Figure 2.1.1.2 Norm of estimation........ 34 Figure 2.1.1.3 Difference between the true y(t) and the last iteration y(t)……35 Figure 2.1.2.1 The cost function .........36 Figure 2.1.2.2 Norm of estimation........ 36 Figure 2.1.2.3 Difference between the true y(t) and the last iteration y(t)……37 Figure 2.1.3.1 The cost function…………………38 Figure 2.1.3.2 Norm of estimation........ 38 Figure 2.1.3.3 Difference between the true y(t) and the last iteration y(t)……391549956 bytesapplication/pdfen-US最佳化控制遞迴演算法狀態估測線性時變系統optimal controlperturbationnonlinear systemiteration algorithmmotion planningthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/61611/1/ntu-93-R91522819-1.pdf