CODES: Cooperative Data-Enabled Extremum Seeking for Multi-Agent Systems

In this paper, we study the problem of model-free cooperative real-time optimization in multi-agent network systems (MAS). Unlike existing adaptive extremum seeking approaches that presume the satisfaction of a persistence of excitation condition on the agents of the network, we propose a novel approach that leverages the presence of cooperation and information-rich data sets in the system. This approach is based on the idea that in MAS with sufficient communication and information resources, agents can efficiently learn a common cost function under mild individual excitation requirements by leveraging cooperation. Therefore, our main result can be seen as a spatiotemporal condition that guarantees model-free optimization in MAS with agents having homogeneous but unknown cost functions. To solve this model-free optimization problem, we characterize a class of robust dynamics that can be safely interconnected with the data-enabled learning mechanism in order to achieve a stable closed-loop system. A numerical result is presented to illustrate the approach.