7 - Robust consensus control of multi-agent systems with input delay

Abstract

In this chapter, we systematically investigate the robust consensus control problem of multi-agent systems with nonlinearity and time delay. To deal with the input delay, model reduction method is employed by a state transformation in the presence of nonlinearity in the agent dynamics. Compensation based on the relative input information is added in the controller design to offset any constant input delay. Due to the limitations of sensors or link failures, sometimes, the relative input information is unobtainable. For such cases, the TPF (short for truncated prediction feedback) approach is adopted to deal with the input delay, and a finite-dimensional TPF controller is constructed for each agent. To tackle the influence of the nonlinear terms under the state transformations, further rigorous analysis is carried out to ensure that the extra integral terms of the system state associated with nonlinear functions are properly considered by means of Krasovskii functionals. By transforming the Laplacian matrix into the real Jordan form, global stability analysis is put in the framework of Lyapunov functions in the real domain. Conditions based on the Lipschitz constant are identified for proposed consensus protocols with/without relative input information to tackle Lipschitz nonlinear terms in the system dynamics. Simulation results show that robust consensus of multi-agent systems with time delay can be achieved under the proposed control protocol.