Adaptive Control Of Nonlinear Multi-agent Systems With Prescribed Performance Via Barrier Lyapunov Function

The research of multi-agent system has been widely used in the real life.When it is hoped that the designed controller can achieve the prescribed performance evaluation of the system,such as given steady synchronization error,maximum error overshoot,and error convergence rate,uncertainties in the system make these difficult to obtain.In order to avoid trial and error experiments,some scholars adopt a kind of prescribed performance control based on transformed error to solve this problem.The controller with introducing transformed error is low-of-complexity and powerful self-adapting.However,due to the strong coupling between nodes and high performance requirements,the controller with introducing transformed error is easy to chattering,which affects the stability of the system.This thesis tries to design a kind of adaptive controller based on the barrier Lyapunov function method,to achieve the prescribed performance of the system and ensure the smoothness of the controller.The specific work and innovation are as follows:The thesis defines a novel distributed barrier Lyapunov function to constrain the errors in the multi-agent systems,and approximate the dynamics' nonlinearities by us-ing neural networks.When designing the controller,the existing chattering terms are introduced into the update law of weights of neural network to avoid being introduced directly into the control input.In this framework,the thesis studies the following prob-lems.1.Firstly,the synchronization problem of a class of nonlinear multi-agent systems,with communication topologies containing directed spanning trees,is considered in this thesis.We use a distributed barrier Lyapunov function to constrain the synchronization errors,and propose a kind of neural network adaptive control based on barrier Lyapunov function.2.The thesis further considers a second-order nonlinear multi-agent systems,with communication topologies containing directed spanning trees.A kind of sliding mode error about the position and velocity synchronization errors is designed,and the barrier Lyapunov function is used to constrain the sliding mode error so as to constrain the synchronization errors.A class of neural network adaptive control based on barrier Lyapunov function is proposed either.3.This thesis considers a class of nonlinear multi-agent systems,with a commu-nication topology of tree structure.It is expected to realize the formation shape while ensuring the connectivity maintenance between agents.Take all the above requirements into account,the upper and low bounds of the relative position error are related to the sensing range and expected relative position.Then the corre-sponding neural network adaptive control based on barrier Lyapunov function is proposed in this thesis.Experimental results show that that the errors in the above problems converge to given bounds at rates not less than predefined values by using the designed control laws,and the control laws are smooth.