臺灣博碩士論文加值系統

於此論文，我們研究Hamilton-Jacobi-Bellman(HJB)方程的理論及數
值解。我們一方面是以動態規劃原理及黏滯解的角度去探討HJB方程的
理論，而另一方面，是採用Wang-Gao-Teo 數值法去計算HJB方程的數值解。最後，我們將這些技巧應用到含有輸出參考信號的追蹤問題。

The theory and the numerical approximation of Hamilton-Jacobi-Bellman (HJB) equations are investigated in this thesis. We discuss the theory of HJB equation via dynamical programming principle and viscosity solution. Further, the solution of HJB equations is approximated numerically via the Wang-Gao-Teo scheme. Finally, we apply the results of the HJB theory together with the Wang-Gao-Teo scheme to solve the command-tracking problem that involves achieving a desired trajectory.

Contents
摘要 Ⅰ
Abstract Ⅱ
誌謝 Ⅲ
List of Figures Ⅳ
List of Table Ⅴ
Notations Ⅵ
1 Introduction 1
2 HJB Theory 3
2.1 Optimal control and HJB equation 3
2.2 Viscosity solution of HJB equation 17
3 Numerical Solution Scheme 22
3.1 The Wang-Gao-Teo scheme 22
3.2 The computational domain 28
4 Illustrative Examples and Command Tracking Application 31
4.1 Verification test 31
4.2 Two dimensional value function 38
4.3 Constant command tracking problem 40
5 Conclusions 44
References 45
Appendix A: Matlab Code for Example 1 47
Appendix B: Matlab Code for Example 2 53
Appendix C: Matlab Code for Example 3 57
Appendix D: Matlab Code for 2D Value Function 63

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