Performance-oriented design and analysis for direct data-driven control of multi-agent systems

There exists a relationship between the consensus performance and the control protocol in the coordination of multiple agents. This article proposes a novel direct data-driven control (DirDDC) using such a relationship directly by establishing a performance-oriented design and analysis framework without relying on any model information. A consensus error is defined by considering the topology information among the agents to match the consensus objective. Then, a nonlinear data relationship between the consensus-error and control input (NDR-CE&I) is established such that the current consensus error is related to the previous consensus errors and the agent inputs over a moving time window. Next, a linear data relationship of NDR-CE&I, termed as LDR-CE&I, is established by introducing a dynamic linearization method. Subsequently, the novel DirDDC is proposed directly using the LDR-CE&I regardless whether the multi-agent systems (MASs) are nonlinear or linear, affine or non-affine, homogeneous or heterogeneous. The convergence analysis is directly conducted based on the performance function, i.e., the NDR-CE&I, instead of the original MASs, so that the model requirement of the MASs can be completely bypassed. The proposed DirDDC can be applied to the MASs with either fixed or switching communication topologies. The simulation study verifies the results.