Necessary optimality conditions for optimal control problems with mixed state-control equality constraints are obtained. The necessary conditions are given in the form of a weak maximum principle and are obtained under (i) a new regularity condition for problems with mixed linear equality constraints and (ii) a constant rank type condition for the general non-linear case. Some instances of problems with equality and inequality constraints are also covered. Illustrative examples are presented.

中文翻译：

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恒定秩条件下具有混合约束的最优控制问题的弱最大原理

获得了具有混合状态控制等式约束的最优控制问题的最优条件。必要条件以弱最大原理的形式给出，并且是在（i）具有混合线性等式约束的问题的新规则性条件和（ii）对于一般非线性情况的恒定秩类型条件下获得的。涉及平等和不平等约束问题的一些实例也包括在内。给出了说明性示例。