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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具有bang-bang解的凸最优控制问题的梯度投影法的收敛性。


我们在具有爆炸式解决方案的非线性最优控制问题的框架中重新审视梯度投影方法。我们获得了控制迭代序列和相应轨迹的强收敛性。此外，我们根据相应切换函数中出现的常数建立收敛速度，并证明该收敛速度估计是尖锐的。一些数值说明证实了理论结果。