Optimization-based Control with Population Dynamics for Large-scale Complex Systems
The motivation in this doctoral thesis proposal is to work on these two different topics (optimization-based control and evolutionary game theory), which are currently object of research in the control systems area, and complement these theories each other to propose a solution for non-centralized control systems design. There are two approaches to work with game theory that will be studied in this thesis. In the first approach, game theory is used as the unique element in the design of controllers. In this sense, game theory works as a tool for an optimization-based control design. Moreover in the second approach, game theory is used to complement an existing
control strategy (e.g., coordinating different local elements of the controller, making dynamical tuning in a multi-objective controller, designing observers, etc). In this case, game theory acts as part of the optimization-based controller. This work proposes to study, develop and implement optimization techniques based on evolutionary game theory, since this theory allows to model a set of elements that have behavioral rules and that interact each other to achieve a global and common objective (e.g., the maximization/minimization of a cost function). In this way, this theory could be adapted to solve engineering problems, in particular the large-scale complex systems. Besides, by making an analogy, there might be an appropriate set up for populations to be associated to partitions in a large-scale complex systems, and the fact elements act according to individual rules can be developed to design non-centralized models (models in which these decisions are computed by local controllers). Finally, the global objective is related to a cost function satisfying a resource constraint.
The work is under the scope of the following projects: