A Hybrid Bellman Equation for systems with regional dynamics
A Hybrid Bellman Equation for systems with regional dynamics
复制标题
区域动力学系统的混合贝尔曼方程
DOI：
10.1109/cdc.2007.4434952
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
R. Malhamé
中科院分区：
文献类型：
--
作者：
Angela P. Schoellig;P. Caines;M. Egerstedt;R. Malhamé
在本文中，我们研究的混合系统与区域动态，即，当系统的连续状态到达给定的切换表面时，在不同的动力学状态之间发生转换的系统。特别是，我们把注意力集中在最优控制问题与这样的系统，我们提出了一个混合Bellman方程，这样的系统，提供了一个表征的全局最优性，开关的数量上界。毫不奇怪，解决方案将是混合的性质，因为它将不仅取决于连续的控制信号，而且还取决于离散的决定，即系统首先应该通过什么域。一些例子来突出所提出的方法的操作。
In this paper, we study hybrid systems with regional dynamics, i.e., systems where transitions between different dynamical regimes occur as the continuous state of the system reaches given switching surfaces. In particular, we focus our attention on the optimal control problem associated with such systems, and we present a Hybrid Bellman Equation for such systems that provide a characterization of global optimality, given an upper bound on the number of switches. Not surprisingly, the solution will be hybrid in nature in that it will depend on not only the continuous control signals, but also on discrete decisions as to what domains the system should go through in the first place. A number of examples are presented to highlight the operation of the proposed approach.