THE SWITCH POINT ALGORITHM
THE SWITCH POINT ALGORITHM
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DOI：
10.1137/21m1393315
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发表时间：
2021-01-01
影响因子：
2.2
通讯作者：
Hager, William W.
中科院分区：
文献类型：
--
作者：
Aghaee, Mahya;Hager, William W.
切换点算法是一种求解最优控制问题的新方法，它的解是奇异的或bang-bang的，或奇异和bang-bang的，并且在解结构发生变化的时刻，最优控制中具有有限个跳跃间断。这类问题通常可以简化为对切换点的优化。推导出目标相对于切换点、初始余态和终端时间的导数公式。所有这些衍生物可以同时计算在一个集成的状态和协态动态。因此，基于梯度的无约束优化技术，包括共轭梯度法或拟牛顿法，可以用来计算最优控制。该算法的性能说明使用测试问题与已知的解决方案，并与其他算法从文献中的比较。
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.