Optimization with Monte Carlo methods for the control of complex systems

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.

In the period of the project, the PI will strengthen links with the Air Traffic Management (ATM) industry through the EU iFly project. The results of this project will be, although not directly within the time frame of the project, a substantial contribution towards the deployment of new reliable routing algorithms which can sustain the performance of the European ATM in accommodating, with safety, the steady growth of air traffic in Europe and worldwide. In modern society, the safety and efficiency of air traffic have major beneficial effects on the economy, the quality of life and the environment. In addition, the PI plans to organize a study day on the topic adaptive design of clinical trials'' in collaboration with Professor Keith Abrams of the Department of Health Sciences of the Leicester Medical School. The adaptive approach to clinical trials involves the sequential optimization of the design of a clinical trial on the basis of accumulated data. Timeliness of applied research on this topic arises from the strong need to make drug development more efficient, safer and yet faster. The purpose of this initiative is to explore the possibility of collaboration between researchers active in optimization decision and control in Engineering, Bayesian statisticians, health economists and researchers from the industry. The adaptive approach is being used increasingly in the development of new drugs because it greatly enhances the efficiency of the clinical trials in terms of costs and effective treatment of patients. The impetus for the use of adaptive trials is supported by the Food and Drug Administration (FDA), and by the European Medicines Agency, respectively the drug regulators in the US and in Europe. The application to clinical trials fits also with the EPSRC theme `Towards Next-generation Healthcare'.