Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE credits
In this thesis, general problems are considered where a group of agents should autonomously position themselves in such a way that a global objective function is maximized, whereas each agent uses only the measurement of its own utility function.
Specially constructed extremum seeking schemes for single and multi-agent systems are presented, where the agents have only access to the current value of their individual utility functions and do not know the analytical model of the global or local objectives. By using an approximative system that is calculated using a methodology based on Lie brackets, practical stability of an equilibrium point is proved for the single agent as well as for the multi-agent case. The motion dynamics of the agents are modeled as single integrators, double integrators and unicycles.
A potential game approach is used in order to deduce conditions under which the whole group of agents converges to a region arbitrary close to the maximum of a global objective function, that coincides with the Nash equilibrium of the game.
As an application of the proposed algorithms, the sensor coverage problem is introduced. In this problem, a group of autonomous sensors is meant to position themselves such that a certain region is covered optimally, in the sense that the amount of detected events appearing in this region, is maximized. The problem is interpreted as a potential game where individual utility functions for each sensor are constructed in a way suitable for the direct application of the proposed optimization methodology.
2010. , 105 p.