Distributed consensus control of periodically time-varying multi-agent systems using neural networks and fourier series expansion

This paper studies the consensus of nonlinear multi-agent systems with periodic disturbances and uncertain dynamics based on matrix theory, adaptive control, neural networks and fourier series expansion. Firstly, fourier series expansion and neural networks are used to describe the unknown periodic time-varying parameter and uncertain nonlinear dynamic, respectively. Secondly, based on adaptive control technology and reparameterization method, two new fully distributed control protocols are designed based on symbolic function and smooth hyperbolic tangent function, respectively, so that all agents can reach asymptotic consensus. Thirdly, a new positive integral bounded function is introduced to compensate for the approximation error caused by the smooth hyperbolic tangent function instead of the symbolic function, so that all network nodes achieve the same consensus effect. Finally, a simulation example is given to verify the effectiveness of the two algorithms and to illustrate their advantages and disadvantages.