Integrated Adaptive Protocols for Consensus Tracking with Lipchitz Nonlinear Dynamics

This article proposes an integrated adaptive control approach to solving the consensus tracking problem of multiagent systems with Lipchitz nonlinear dynamics. By extending the adaptive law from scalar form to matrix form, only one adaptive coupling gain matrix is employed to adjust the feedback control gain and coupling weight simultaneously, which provides considerable convenience for analysis and application of the consensus tracking protocol. Theoretical identification of the effectiveness of the integrated design approach is presented by using the Lyapunov stability theory with the Lyapunov function partly constructed by the trace-norm of the adaptive coupling gain matrix. Furthermore, the integrated adaptive control approach is extended to achieve robust consensus tracking with a leader having nonzero inputs. For bounded disturbances, the ultimate boundedness of the consensus error is ensured by using the σ modification technique. For L_2-type disturbances, a desirable disturbance rejection performance is guaranteed by applying the H∞ control method. A numerical example of forced pendulums is given to illustrate the effectiveness of the proposed consensus protocol.