Tailored Mixed-Integer Optimal Control policies for real-world applications usually have to avoid very short successive changes of the active integer control. Minimum dwell time (MDT) constraints express this requirement and can be included into the combinatorial integral approximation decomposition, which solves mixed-integer optimal control problems (MIOCPs) to $$\epsilon $$ -optimality by solving one continuous nonlinear program and one mixed-integer linear program (MILP). Within this work, we analyze the integrality gap of MIOCPs under MDT constraints by providing tight upper bounds on the MILP subproblem. We suggest different rounding schemes for constructing MDT feasible control solutions, e.g., we propose a modification of Sum Up Rounding. A numerical study supplements the theoretical results and compares objective values of integer feasible and relaxed solutions.

中文翻译：

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最小停留时间约束下的混合整数最优控制

为实际应用量身定制的混合整数最优控制策略通常必须避免活动整数控制的非常短的连续变化。最小驻留时间 (MDT) 约束表达了这一要求，并且可以包含在组合积分近似分解中，该分解通过求解一个连续非线性程序和一个混合整数将混合整数最优控制问题 (MIOCP) 求解为 $$\epsilon $$-最优-整数线性规划（MILP）。在这项工作中，我们通过提供 MILP 子问题的严格上限来分析 MIOCP 在 MDT 约束下的完整性差距。我们为构建 MDT 可行控制解决方案提出了不同的舍入方案，例如，我们提出了 Sum Up Rounding 的修改。