论文标题
具有直接搭配和可变离散化的时间优势控制
Time-optimal control with direct collocation and variable discretization
论文作者
论文摘要
本文涉及基于直接搭配的非线性连续时间系统的时间优势控制。基本离散网格的时间在时间上是可变的，因为时间间隔会进行优化。该技术不同于通常基于时间转换的方法。在最佳控制和轨迹优化领域，选择了Hermite-Simpson搭配为共同代表。在此，二次花键近近似系统动力学。几个不同顺序的花链适合控制参数化。比较分析表明，增加了控制自由度，例如二次样条纹不适用于由于违反限制和固有振荡而导致的时间优势控制问题。但是，选择恒定或线性控制花键指出非常有效。一个主要的优点是，系统动力学的隐式解决方案适用于刚性系统，并且在实践中通常需要较小的网格尺寸。
This paper deals with time-optimal control of nonlinear continuous-time systems based on direct collocation. The underlying discretization grid is variable in time, as the time intervals are subject to optimization. This technique differs from approaches that are usually based on a time transformation. Hermite-Simpson collocation is selected as common representative in the field of optimal control and trajectory optimization. Hereby, quadratic splines approximate the system dynamics. Several splines of different order are suitable for the control parameterization. A comparative analysis reveals that increasing the degrees of freedom in control, e.g. quadratic splines, is not suitable for time-optimal control problems due to constraint violation and inherent oscillations. However, choosing constant or linear control splines points out to be very effective. A major advantage is that the implicit solution of the system dynamics is suited for stiff systems and often requires smaller grid sizes in practice.
