论文标题
开关点算法
The Switch Point Algorithm
论文作者
论文摘要
开关点算法是解决最佳控制问题的一种新方法，其解决方案是单数或爆炸或单数和爆炸式和bang-bang的方法，并且在解决方案结构变化的时间点上具有最佳控制点中具有有限数量的跳跃不连续性。该课程中的问题通常可以简化为对开关点的优化。针对开关点，初始倒计和终端时间的目标导数得出了公式。所有这些衍生物只能在状态和昂贵的动态的一个集成中同时计算。因此，可以使用基于梯度的不受约束的优化技术，包括共轭梯度方法或准Newton方法，可用于计算最佳控制。使用已知解决方案的测试问题和与文献中的其他算法进行比较来说明该算法的性能。
The Switch Point Algorithm is a new approach for solving optimal control problems whose solutions are either singular or bang-bang or both singular and bang-bang, and which possess a finite number of jump discontinuities in an optimal control at the points in time where the solution structure changes. Problems in this class can often be reduced to an optimization over the switching points. Formulas are derived for the derivative of the objective with respect to the switch points, the initial costate, and the terminal time. All these derivatives can be computed simultaneously in just one integration of the state and costate dynamics. Hence, gradient-based unconstrained optimization techniques, including the conjugate gradient method or quasi-Newton methods, can be used to compute an optimal control. The performance of the algorithm is illustrated using test problems with known solutions and comparisons with other algorithms from the literature.
