Quantum mechanics

Mean square

Control (management)

Multi-agent system

Dynamics (music)

Laplace operator

Consensus

Square (algebra)

Applied mathematics

Eigenvalues and eigenvectors

Economics

Computer science

Acoustics

Protocol (science)

Lipschitz continuity

Alternative medicine

Physics

Nonlinear system

Mathematics

Lyapunov function

Mathematical analysis

Artificial intelligence

Geometry

Medicine

Finance

Laplacian matrix

Control theory (sociology)

Order (exchange)

Pathology

IEEE Transactions on Systems Man and Cybernetics Systems

This paper focuses on the mean square practical leader-following consensus of second-order nonlinear multiagent systems with noises and unmodeled dynamics, where all agents are influenced by noises emerging from the input channels. We present a new distributed protocol, which contains a designed signal to dominate the effects of unmodeled dynamics, to solve the mean square leader-following consensus problem for the nonlinear multiagent systems. The protocol is designed without using any global information, even the eigenvalues of the Laplacian matrix. The Lipschitz constant of the nonlinear function is also unknown to all followers. Using the Lyapunov functional approach and the stochastic theory, it is proven that the mean square practical leader-following consensus is achieved by the designed protocol. Finally, two examples are provided to illustrate the effectiveness of the designed algorithm.

Mean Square Leader–Following Consensus of Second-Order Nonlinear Multiagent Systems With Noises and Unmodeled Dynamics