求解最优控制问题的改进辛几何算法

最优控制问题的 Pontryagin极大值原理以 Hamilton形式为基石 ,合理的数值计算应当遵循 Hamilton体系的性质 ,而以 Runge- Kutta( R- K)方法为代表的传统计算方法却不能保持这一性质 .本文尝试用基于 Hamilton体系的辛几何算法求解最优控制问题 ,提出了消除计算过程中误差生长的方法 ,最后设计了仿真算例 ,与 R- K法相比显示了明显的优越性

Improved Symplectic Method for Solving Optimal Control Problems

The maximum principle of Pontryagin for solving optimal control problem is based on Hamiltoni- an form,a reasonable numerical computation method must be in conformity with the characteristics of Hamiltonian system.In fact,the traditional computation methods represented by Runge- Kutta method are not based on Hamiltonian system.In this paper,the symplectic method,which is suitable to Hamiltonian system,was presented for solving optimal control problems.The problem about how to avoid the error- growth was also discussed.At the end of this paper,there was an example,from which the superior char- acteristics of sympletic method can be easily found.