Multi‐layer distributed protocols for robust cooperative tracking in interconnected nonlinear multiagent systems

Abstract

SummaryWe develop a mixed graph and optimal control theoretic formulation to design a robust cooperative control protocol for a large‐scale multiagent system with partially known interconnected first‐, second‐, or mixed first‐ and second‐order dynamics. In each case, we transform the control protocol design task to a robust communication graph design problem, which, from a cyber‐physical perspective, is interpreted as the control layer design problem for an interconnected system with unknown agent layer dynamics. According to this viewpoint, each state variable has its own control layer communication topology separate from the other state variable's communication topology and the unknown agent layer interconnection topologies. We prove that all cooperative, decentralized, and centralized tracking protocols can be treated as a single design problem and, by deriving closed‐form solutions for the robust control layer topologies, we further provide a simpler design procedure, which is only based on the matrix manipulations. Aside from the linear implementation of the protocol and the connection of the proposed formulation to the well known rules‐of‐thumb in optimal control theory, this creates a higher potential to transfer ideas to industry. Modeling uncertainties tolerable by a given control layer topology is analyzed, and a preliminary performance‐oriented analysis and design approach for large‐scale interconnected systems is discussed. We show that exactly the same steps can be followed to design appropriate control layers for both tracking and stabilization.