We consider a nonlinear optimal control problem with dynamics described by a nonlinear evolution equation defined on an evolution triple of spaces. Both the dynamics and the cost functional are not convex and so an optimal pair need not exist. For this reason using tools from multivalued analysis and from convex analysis, we introduce a relaxed version of the problem. No Young measures are involved in our relaxation method. We show that the relaxed problem is admissible.

中文翻译：

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非线性发展方程驱动的最优控制问题的松弛

我们考虑具有动力学的非线性最优控制问题，该问题由在空间演化三元组上定义的非线性演化方程描述。动力学和成本函数都不是凸的，因此不需要最优对。因此，我们使用来自多值分析和凸分析的工具，介绍了该问题的一个宽松版本。我们的放松方法不涉及年轻措施。我们表明，宽松的问题是可以接受的。