论文标题
高度振荡系统的有效数值最佳控制
Efficient Numerical Optimal Control for Highly Oscillatory Systems
论文作者
论文摘要
我们提出了一种有效的转录方法，用于高度振荡的最佳控制问题。对于这些问题，最佳状态轨迹由快速振荡组成，这些振荡在时间范围内会缓慢变化。在大量振荡中，我们仅通过构建一个可以与集成步骤集成的半明确差分 - 代数方程来模拟子集以近似缓慢的变化，从而大于一个时期。对于通过直接方法解决最佳控制问题的解决方案，我们提供了一种参数化和正规化控件的方法。最后，我们利用该方法来找到低头卫星的燃油轨道转移。使用新方法，我们将所得非线性程序的大小降低了一个以上的数量级。
We present an efficient transcription method for highly oscillatory optimal control problems. For these problems, the optimal state trajectory consists of fast oscillations that change slowly over the time horizon. Out of a large number of oscillations, we only simulate a subset to approximate the slow change by constructing a semi-explicit differential-algebraic equation that can be integrated with integration steps much larger than one period. For the solution of optimal control problems with direct methods, we provide a way to parametrize and regularize the controls. Finally, we utilize the method to find a fuel-optimal orbit transfer of a low-thrust satellite. Using the novel method, we reduce the size of the resulting nonlinear program by more than one order of magnitude.
