| 利用H-J-B方程的粘性逼近求解非线性最优控制 |
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| 引用本文： | 朱经浩,马婧瑛. 利用H-J-B方程的粘性逼近求解非线性最优控制[J]. 同济大学学报(自然科学版), 2005, 33(7): 947-951 |
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| 作者姓名： | 朱经浩 马婧瑛 |
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| 作者单位： | 同济大学,应用数学系,上海,200092 |
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| 基金项目： | 国家自然科学基金资助项目(10371089) |
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| 摘 要： | 利用李级数离散控制系统，逼近最优轨道，并利用H-J-B方程的粘性逼近估计值函数．进而借助动态规划原理，把非线性最优控制的数值求解转化为一组正定二次规划的求解．对一个非线性的动态规划过程进行线性化的逼近，这在理论上简化了非线性最优控制问题求解的困难，从实际计算数学的角度看，这也将加快非线性最优控制数值解的计算速度。
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| 关 键 词： | 非线性最优控制 李级数 粘性逼近 |
| 文章编号： | 0253-374X(2005)07-0947-05 |
Approximation to Nonlinear Optimal Control by Viscosity Approximation of H-J-B Equations |
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| ZHU Jing-hao,MA Jing-ying. Approximation to Nonlinear Optimal Control by Viscosity Approximation of H-J-B Equations[J]. Journal of Tongji University(Natural Science), 2005, 33(7): 947-951 |
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| Authors: | ZHU Jing-hao MA Jing-ying |
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| Abstract: | In this article,we introduce the idea of using Lie series to give an approximation of the optimal tra- jectory of a nonlinear optimal control problem by a discrete process.The dynamic programming equation is solved by means of the viscosity approximation of value functions and a positive quadratic programming.By this way,a nonlinear dynamic programming is transformed to a linear approximation.The difficulty of solving an op- timal control problem is simplified. |
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| Keywords: | nonlinear optimal control Lie series viscosity approximation |
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