We revisit the gradient projection method in the framework of nonlinear optimal control problems with bang–bang solutions. We obtain the strong convergence of the iterative sequence of controls and the corresponding trajectories. Moreover, we establish a convergence rate, depending on a constant appearing in the corresponding switching function and prove that this convergence rate estimate is sharp. Some numerical illustrations are reported confirming the theoretical results.

中文翻译：

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带有凸点解的凸最优控制问题的梯度投影方法的收敛性。

我们用bang-bang解重新研究了非线性最优控制问题框架中的梯度投影方法。我们获得了迭代控制序列和相应轨迹的强收敛性。此外，我们根据出现在相应开关函数中的常数来建立收敛速度，并证明该收敛速度估计是精确的。报告了一些数字插图，证实了理论结果。