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Efficient multiple objective optimal control of dynamic systems with integer controls

机译：具有整数控制的动态系统的高效多目标最优控制

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摘要

In practical optimal control problems both integer control variables and multiple objectives can be present. The current paper proposes a generic and efficient solution strategy for these multiple objective mixed-integer optimal control problems (MO-MIOCPs) based on deterministic approaches. Hereto, alternative scalar multiple objective optimisation techniques as normal boundary intersection and normalised normal constraint are used to convert the original problem into a series of parametric single objective optimisation problems. These single objective mixed-integer optimal control problems are then efficiently solved through direct multiple shooting techniques which exploit convex relaxations of the original problem. Moreover, these relaxations enable to quickly approximate the final solution to any desired accuracy (without the need of solving integer problems). Consequently, the set of Pareto optimal solutions of the MO-MIOCP can be accurately obtained in highly competitive computation times. The proposed method is illustrated on (i) a testdrive case study with a complex car model which includes different gears and conflicting minimum time-minimum fuel consumption objectives, and (ii) a jacketed tubular reactor case study with conflicting conversion, heat recovery and installation costs.
机译：在实际的最佳控制问题中，可能同时存在整数控制变量和多个目标。本文基于确定性方法，为这些多目标混合整数最优控制问题（MO-MIOCP）提出了一种通用且有效的解决方案策略。迄今为止，使用替代标量多目标优化技术（如法线边界交集和归一化法线约束）将原始问题转换为一系列参数化单目标优化问题。这些单目标混合整数最优控制问题然后通过直接多重射击技术有效地解决，这些技术利用了原始问题的凸松弛。此外，这些放松使得能够快速将最终解决方案近似为任何所需的精度（无需解决整数问题）。因此，可以在竞争激烈的计算时间内准确获得MO-MIOCP的一组Pareto最优解。在以下方面说明了所建议的方法：（i）复杂汽车模型的试驾案例研究，该模型包括不同的档位，并且最小时间-最小燃料消耗目标相互矛盾;（ii）转化，热回收和安装矛盾的夹套式管式反应堆案例研究费用。

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