Research On Cooperative Control For The Three-dimensional Formation Of Multi-agent Systems With Time-delay

In recent years,multi-agent systems has become the frontier topics in the field of control.The application of multi-agent formation control mostly focuses on three-dimensional space in real life.Although some research results on multi-agent formation control have being obtained,the problems about the three-dimensional layered formation control of a large number of multi-level systems and the three-dimensional formation control of multi-agent systems containing nonlinear disturbance items in individual models have not be well resolved.In addition,the time delays in the multi-agent system also cause some difficulties for the design of the distributed controllers.Therefore,the design method of three-dimensional formation and cooperative control of multi-agent systems with time delay are studied.Based on the layered formation theory and RBF neural network theory,the problem of how to realize the three-dimensional formation cooperative control of multi-agent systems with time delay is studied.For the large-scale layered formations,the control protocols for hierarchical formation in three-dimensional space are presented for low-order and high-order multi-agent systems with time delays respectively,so that the multi-agent systems can form the desired three-dimensional hierarchical formation.For the multi-agent systems with nonlinear disturbances,an improved RBF neural network three-dimensional formation control protocol is proposed for multi-agent systems with time delays and nonlinear disturbances.The control protocol ensures that multi-agent systems can form three-dimensional formations,and the formation can follow the desired trajectory function.For the first-order multi-agent systems with time delay,the P controller is designed according to the Nyquist stability criterion.For second-order and higher-order multi-agent systems with time delay,the corresponding PD controller is designed.Firstly,the multiple-input multiple-output coupled system can be decoupled into multiple single-input single-output systems by the matrix theory method.Secondly,the parameter ranges of PD and PID controllers which can make each subsystem be stable are obtained based on the D-segmentation method.Finally,the parameter ranges of the multi-agent system can be determined by obtaining the intersection of the stability ranges of the subsystems.An improved RBF neural network three-dimensional formation control method is proposed for multi-agent systems with time-delay and nonlinear disturbances.At first,the nonlinear disturbances are added to the individual model.Based on the good approximation ability of the neural network to nonlinear disturbances,we improve the Gaussian kernel function in the neural network.Then,the part of the system with nonlinear interference and time delay are fitted by using the improved RBF neural network.At last,the improved RBF neural network three-dimensional formation controller protocol design is proposed combining formation control theory and Lyapunov stability criterion.Based on the virtual robot software V-REP,the three-dimensional layered formation control of the quadrotor system is implemented,and the three-dimensional formation control of the quadrotor is implemented using the improved RBF neural network.According to the results of the three-dimensional layered formation experiments,the stability of the system can be guaranteed by selecting the control parameters within the stability domain arbitrarily,thus enabling the four-rotor system to realize three-dimensional stratification and formation.According to the improved RBF neural network three-dimensional formation experimental results,the designed neural network formation control protocol can ensure that the multi-agent system form the three-dimensional formation and move follow the trajectory function.In this paper,the three-dimensional formation method of multi-agent system with time delay are simulated and experimented,and the results show that the proposed method can achieve three-dimensional hierarchical formation of large-scale multi-agent systems and three-dimensional formation of multi-agent systems with nonlinear interference.The research results provide an effective and practical approach to the formation control of multi-agent systems in practical applications.