论文标题
强大的最佳控制使用动态编程和保证Euler的方法
Robust optimal control using dynamic programming and guaranteed Euler's method
论文作者
论文摘要
基于集合的集成方法允许证明差异系统的属性，这些系统考虑到有限的干扰。据说满足此类特性的系统（时间二散，时间连续或杂种）是“健壮的”。在最佳控制综合的背景下，基于设定的方法通常是两个类的数值最佳方法的扩展：首先，基于凸优化的方法；其次，基于动态编程原理的方法。海曼等人。最近表明，对于某些低维系统，第二种数值方法比第一个方法可以提供更好的解决方案。他们已经建立了一个实现这两种数值方法的求解器（BOCOP）。我们在本文中表明，使用保证的Euler集成方法的第二类方法的基于集合的扩展，使我们能够找到如此良好的解决方案。此外，这些解决方案享有在初始条件和有限的干扰上对不确定性的鲁棒性的特性。我们在数值bocop求解器的示例中证明了我们方法的实际兴趣。我们还提供了我们方法的变体，灵感来自模型预测控制方法，该方法使我们能够以失去鲁棒性的价格更有效地找到最佳控制。
Set-based integration methods allow to prove properties of differential systems, which take into account bounded disturbances. The systems (either time-discrete, time-continuous or hybrid) satisfying such properties are said to be "robust". In the context of optimal control synthesis, the set-based methods are generally extensions of numerical optimal methods of two classes: first, methods based on convex optimization; second, methods based on the dynamic programming principle. Heymann et al. have recently shown that, for certain systems of low dimension, the second numerical method can give better solutions than the first one. They have built a solver (Bocop) that implements both numerical methods. We show in this paper that a set-based extension of a method of the second class which uses a guaranteed Euler integration method, allows us to find such good solutions. Besides, these solutions enjoy the property of robustness against uncertainties on initial conditions and bounded disturbances. We demonstrate the practical interest of our method on an example taken from the numerical Bocop solver. We also give a variant of our method, inspired by the method of Model Predictive Control, that allows us to find more efficiently an optimal control at the price of losing robustness.
