Game-theoretic methods for control of large-scale systems

A theory that seems to be particularly applicable to tackle these problems is the theory of the Stackelberg and inverse Stackelberg games, because in these games the hierarchy plays an important role.

The inverse Stackelberg games are leader-follower games in which the leader announces his strategy as a mapping from the follower's decision space into his own decision space, while taking the possible reactions of the follower into account. The leader and the follower may have different and often conflicting objectives. Morover, the game may involve multiple leaders and followers. The inverse Stackelberg games can be thought of as a generalization of classical Stackelberg games. The problem of finding the optimal strategy for the leader belongs to the realm of composed functions and these problems are known to be very difficult to solve in an analytic way.

While there are many applications having the inverse Stackelberg game character, only a little amount of theory is known about such problems and the theory that does exist is still in its infancy, focusing on exploring specific phenomena by means of case studies. Little is known about general properties of such games as well as about the inverse Stacklelberg games with incomplete information.

This project includes the following three phases:

In the first phase several case studies are considered. In these case studies optimization and control system theory techniques (e.g. the Pontryagin minimum principle, the Ricatti equations, or finding the optimal strategy within the prespecified class of functions and showing the global optimality of such a strategy a posteriori) are used in order to obtain the global solution, preferably in a closed form.

The second phase of the research focuses on game-theoretic methods that could be employed for modeling communication and interaction between the various control levels in the control of large-scale systems. The Stackelberg type of games seems to be a natural framework to apply here, although this hypothesis still has to be validated.

In the third phase of the research the proposed game theoretic methods are applied in road traffic control.