求解非光滑最优控制问题的自适应网格优化

Adaptive mesh refinement for solving non-smooth optimal control problems

针对传统直接配点法在求解非光滑最优控制问题时存在离散误差大、精度低的问题,提出了一种自适应直接配点法。利用局部分段插值多项式逼近最优解,将最优控制问题离散为非线性规划问题,并给出了离散误差估计方法,根据离散误差的大小确定区间内节点的加密量,提出了自适应网格优化算法,利用该算法将大部分节点配置在非光滑区域以降低离散误差。最后通过仿真算例将所提算法与传统直接配点法和文献中的拟谱自适应算法分别进行比较,验证了所提算法的高精度和有效性。

Due to the large discrete errors and low accuracy of the conventional direct collocation method for solving non-smooth optimal control problems, an adaptive direct collocation method is presented. The optimal control problem is transcribed into a nonlinear programming problem by using local piecewise interpolation poly nomials to approximate the optimal solution. The estimation method of discrete errors is also presented, and an adaptive mesh refinement algorithm is used to refine the grid by adding nodes to the segments in which the opti mal solution is non-smooth, the algorithm is repeated until a user-specified error tolerance is met. Finally, the simulation results demonstrate the utility and efficiency of the proposed method by comparing it with the con- ventional direct collocation method and the adaptive pseudospectral algorithm respectively.