Bipartite Consensus Control For Lower-Triangular Nonlinear Multi-Agent Systems

In recent years,the consensus control of multi-agent systems has received extensive attention from many scholars and has been successfully applied in aerospace,intelligent transportation,and other fields.Compared with linear multi-agent systems,lower-triangular nonlinear multi-agent systems can describe many complex practical engineering systems more accurately,so it is more practical to study their consensus control problems.At present,fruitful research results have been obtained for the consensus control problem of lower-triangular nonlinear multi-agent systems.However,most existing results assume that consensus is achieved through cooperative interactions among the agents,often ignoring the possibility of competitive/adversarial interactions.In real situations,cooperation and competition between agents coexist more commonly,and examples such as two-way drone flights,fleet cruises,and soccer robot competitions show that the bipartite consensus control problem is more relevant.Consequently,this thesis investigates the bipartite consensus control problem of lower-triangular nonlinear multi-agent systems under cooperative-competitive networks.The main research contents of the thesis are as follows:1.For the lower-triangular nonlinear multi-agent systems with unknown control coefficients,the output bipartite consensus control problem is studied by the backstepping design method.First,the positive productable function is introduced and combined with the neural network technique to deal with the effects of uncertainties,such as the nonlinear terms of the system and the unknown control coefficients.Second,the backstepping design method is applied to design an adaptive state feedback control protocol based on the radial basis function neural network.Finally,the appropriate function is constructed to prove the asymptotic convergence of the bipartite consensus error of the system output without using the upper bound of the miknown control coefficients.2.For the lower-triangular nonlinear multi-agent systems with dead-zone,external disturbance,and input delays,the backstepping design method is combined with the dynamic surface control technique to investigate the output bipartite consensus control problem.First,the dead-zone input is properly modeled,and an auxiliary system is introduced to compensate for the dead-zone and input delays.Second,the unknown nonlinear terms of the system are estimated with the help of the neural network technique,and perturbation observers are designed based on the auxiliary system to eliminate the effects of disturbance and estimation error.Then,the adaptive state feedback control protocol is designed by using the dynamic surface control method to effectively overcome the "complexity explosion"problem of the traditional backstepping design approach.Finally,the appropriate function is constructed to prove that the designed control protocol can guarantee the boundedness of the system output bipartite consensus error.3.For the lower-triangular nonlinear multi-agent systems with state delays,the output feedback bipartite consensus control problem is studied by the time-varying gain design method under the condition that only the system output is measurable.First,the distributed compensator is constructed using the output information of the agent itself and its neighbors.Second,the output feedback control protocol with time-varying gain is proposed based on the compensator,where the time-varying gain can compensate for the unknown growth rate in the nonlinear term of the system.Finally,the appropriate Lyapunov function is constructed to prove the asymptotic convergence of the bipartite consensus error.