Distributed fuzzy tracking for multi-agent systems

This paper proposes a systematic analysis for a stabilisation/tracking problem in a network of nonlinear systems. A reasonably general class of nonlinear systems is considered in their equivalent Takagi-Sugeno (TS) representation. Due to the structure, properties and reduced mathematical complexity of the TS approach, a decoupling of the network into node level dynamics is achieved which simplifies the stability analysis and the design of a control law. A distributed control law is introduced which is composed of both node and network level information. The design involves two stages. Firstly feedback gains are synthesized for the isolated agents ignoring interconnections. Then utilising a common Lyapunov matrix, from the first step, using the relative differences in the states of the agents at network level, co-operative behaviour among the agents is introduced. This is all performed subject to design criteria, posed as Linear Matrix Inequalities (LMIs). The benefits of this analysis is that the design of the controller is decoupled from the size and topology of the network, and it allows a convenient choice of feedback gains for the term that is based on the relative state information. An illustrative example is included to outline the potential of the analysis.