Sufficient optimality conditions for optimal control problems involving isoperimetric and mixed inequality and equality constraints are derived. The main novelty of our approach is the fact that, for such problems, discontinuous and singular solutions can be detected. In other words, our result can deal with solutions for which the proposed optimal control is not continuous, but only essentially bounded, and the classical, crucial strengthened Legendre-Clebsch condition is no longer imposed.

中文翻译：

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最优控制中的基本有界性和奇异性

推导了针对最优控制问题的充分等价条件，这些问题涉及等压和混合不等式和相等约束。我们的方法的主要新颖之处在于，对于此类问题，可以检测到不连续和奇异的解决方案。换句话说，我们的结果可以处理所提出的最优控制不是连续的，而仅是本质上有界的解决方案，并且不再施加经典的，至关重要的强化勒让德-克莱布施条件。