Optimization with Monte Carlo methods for the control of complex systems

在这个项目中，我们将解决最优决策的问题。特别是，我们将开发一个新的框架，使最佳的顺序决策在复杂的问题与不确定的情况。在文献中，存在蒙特卡罗随机优化方法，其中通过对许多可能的结果进行模拟来面对复杂性。这些方法可以找到一个解决方案，一个复杂的决策问题，这是保证在所需的公差，在统计意义上是最佳的。在这里，我们将研究将这些方法的使用扩展到做出最优顺序决策的问题。特别是，我们将建立在何种条件下，可以保证重复使用蒙特卡洛随机优化计算控制决策的复杂动态系统，以导致一个稳定的（安全和可预测的）行为。因此，这个项目将建立一个新的随机优化和控制理论之间的联系。这项工作有许多潜在的应用领域，包括运输和保健部门。

In this project we will address the problem of making optimal decisions. In particular, we will develop a novel framework to make optimal sequential decisions in complex problems with uncertain scenarios. In the literature, there exists Monte Carlo stochastic optimization methods in which complexity is faced by performing simulations of many possible outcomes. These methods can find a solution, to a complex decision problem, which is guaranteed to be optimal within the desired tolerance, in a statistical sense. Here, we will look at extending the use of these methods to the problem of making optimal sequential decisions. In particular, we will establish under which conditions the repeated use of Monte Carlo stochastic optimization for computing control decisions for a complex dynamical systems can be guaranteed to lead to a stable (safe and predictable) behavior. Thus, this project will establish a novel link between stochastic optimization and control theory. The work has a number of potential application areas including the transport and health-care sectors.