We consider mixed-integer optimal control problems with combinatorial constraints that couple over time such as minimum dwell times. We analyze a lifting and decomposition approach into a mixed-integer optimal control problem without combinatorial constraints and a mixed-integer problem for the combinatorial constraints in the control space. Both problems can be solved very efficiently with existing methods such as outer convexification with sum-up-rounding strategies and mixed-integer linear programming techniques. The coupling is handled using a penalty-approach. We provide an exactness result for the penalty which yields a solution approach that convergences to partial minima. We compare the quality of these dedicated points with those of other heuristics amongst an academic example and also for the optimization of electric transmission lines with switching of the network topology for flow reallocation in order to satisfy demands.

我们考虑具有组合约束的混合整数最优控制问题，这些约束随着时间的流逝而耦合，例如最小停留时间。我们分析了一种无组合约束的混合整数最优控制问题和控制空间中组合约束的混合整数问题的提升和分解方法。这两个问题都可以使用现有方法非常有效地解决，例如采用求和四舍五入策略的外凸和混合整数线性规划技术。使用惩罚方法来处理耦合。我们提供了惩罚的精确度结果，从而产生了一种收敛到部分极小值的解决方案。