一种快速高效的控制向量参数化优化方法

A Fast and Efficient Control Vector Parameter Optimization Method

为了更合理地划分动态优化问题离散时间网格,解决控制向量参数化方法逼近精度和计算时间之间的矛盾,提出一种高效的非均匀自适应网格精细化控制策略。通过斜率分析控制参数的变化趋势,对斜率较小的时间节点进行合并,剔除不必要的离散网格;对不同变化趋势的时间网格插入数量不等的时间节点,提高函数逼近的精度。并且结合变时间节点技巧,找到准确的切换时间节点,确保求解的准确性。通过2个经典实例验证了所提方法的有效性。与传统控制向量参数化方法对比,计算成本较低,并可获得更准确的优化结果。

In order to divide the discrete time grid of dynamic optimization problem more reasonably, and to solve the contradiction between approximation accuracy and calculation time of control vector parameterization method, an efficient non-uniform adaptive mesh refinement control strategy is proposed. By analyzing the trend of the control parameters by slope analysis, the time nodes with smaller slopes are combined to eliminate unnecessary discrete meshes;the time grids with different variation trends are inserted into time nodes with different numbers to improve the accuracy of function approximation. And combined with the technique of the variable time nodes, the accurate switching time nodes are found to ensure the accuracy of the solution. The effectiveness of the proposed method is verified by two classical complex examples, compared with the traditional control vector parameterization method, the calculation cost is lower and more accurate optimization results can be obtained.