论文标题
连续优化通过时间冻结来控制具有滞后的混合系统
Continuous Optimization for Control of Hybrid Systems with Hysteresis via Time-Freezing
论文作者
论文摘要
本文介绍了使用非线性优化的技术对具有磁滞的一类混合系统的数值最佳控制，而没有任何整数变量。磁滞是一种独立的记忆效应，通常会导致动力学的严重非平滑度。这些系统不仅仅是分段平滑系统（PSS）；它们是混合系统的更复杂形式。我们介绍了暂时的重新印象，将这些系统转化为PSS。从理论方面，这种重新制定通过为Filippov Systems开发的丰富工具开辟了研究系统的大门。从实用的一侧，它可以使用开关检测的最近开发的有限元[Nurkanovic等，2022]，从而使高精度的数值最佳控制具有滞后性的混合系统。我们提供了一个时间最佳控制问题示例，并比较了文献中的混合制剂配方的方法。
This article regards numerical optimal control of a class of hybrid systems with hysteresis using solely techniques from nonlinear optimization, without any integer variables. Hysteresis is a rate independent memory effect which often results in severe nonsmoothness in the dynamics. These systems are not simply Piecewise Smooth Systems (PSS); they are a more complicated form of hybrid systems. We introduce a time-freezing reformulation which transforms these systems into a PSS. From the theoretical side, this reformulation opens the door to study systems with hysteresis via the rich tools developed for Filippov systems. From the practical side, it enables the use of the recently developed Finite Elements with Switch Detection [Nurkanovic et al., 2022], which makes high accuracy numerical optimal control of hybrid systems with hysteresis possible. We provide a time optimal control problem example and compare our approach to mixed-integer formulations from the literature.
