Game theory for the control of large-scale systems
Other Mentor(s):N.B. Groot
Keywords:Distributed and large-scale systems; Optimization and algorithms for control
Description:One of the major challenges in the control of large-scale intelligent infrastructures such as road traffic networks is to find an efficient optimization scheme that results in a good performance. As a centralized approach will in general not be feasible due to computational issues and a decentralized approach may return an insufficient performance, an approach could be to focus on a multi-level framework in which decisions by several controllers on different, mutually interacting control layers are taken into account. As compared to the hierarchical top-down approach, we however like to increase the decision power of the lower-level controllers.
We currently investigate adopting game-theoretic elements in the modeling of communication and interaction between controllers on the various control levels. A theory that seems to be particularly applicable to tackle these problems is the theory of reverse Stackelberg games.
Reverse Stackelberg games are defined on the basis of a hierarchy between players; a player called the leader acts first by announcing her strategy as a mapping of the follower's decision space into her own decision space (the `leader function'), while taking the response of the follower into account.
Since the problem of finding an optimal strategy for the leader belongs to the realm of composed functions, these problems are known to be very difficult to solve in an analytic way.
Our aim is therefore to develop a solid framework for multi-level control based on the reverse Stackelberg game, which can moreover be efficiently applied to real-life problems.
This Msc project will be aimed towards the investigation of the numerical solvability of several types of reverse Stackelberg problems, with potential applications in traffic control.
After obtaining an understanding of reverse Stackelberg games and of the use of this particular game in control problems, we will investigate different solution methods.
Here, the complexity of small problems will be (empirically) investigated, starting from simple structures of the leader function and working towards more complex structures.