论文标题
控制理论中稳定流形的符号算法
Symplectic algorithms for stable manifolds in control theory
论文作者
论文摘要
在本说明中，我们为汉密尔顿 - 雅各比方程的稳定流形提出了一种符号算法，并结合了[sakamoto-van〜der schaft，IEEE交易，自动控制上的IEEE交易，2008年]。我们的算法包括两个关键方面。第一个是证明收敛半径和局部近似稳定歧管的误差的精确估计。第二个是通过比通用方案更好的长期行为，将局部近似稳定的稳定歧管扩展到较大的歧管。我们的方法避免了近似稳定流形的迭代序列发散的情况，并降低了计算成本。我们通过指数非线性的最佳控制问题来说明算法的有效性。
In this note, we propose a symplectic algorithm for the stable manifolds of the Hamilton-Jacobi equations combined with an iterative procedure in [Sakamoto-van~der Schaft, IEEE Transactions on Automatic Control, 2008]. Our algorithm includes two key aspects. The first one is to prove a precise estimate for radius of convergence and the errors of local approximate stable manifolds. The second one is to extend the local approximate stable manifolds to larger ones by symplectic algorithms which have better long-time behaviors than general-purpose schemes. Our approach avoids the case of divergence of the iterative sequence of approximate stable manifolds, and reduces the computation cost. We illustrate the effectiveness of the algorithm by an optimal control problem with exponential nonlinearity.
