Consensus Control Of Second Order Distributed Parameter Multi-agent System Based On Iterative Learning

Distributed parameter system is a kind of complex system with distributed parameter property,more and more attention has been paid to the related research in thermal engineering,chemical engineering and other fields.Multi-agent system is a kind of complex large-scale system,which is composed of several subsystems.The consensus of multi-agent system is one of the key research issues.Consensus means that the state of each sub-agent system is consistent with the internal information exchange of the adjacent agents in the multi-agent system.Its research focus is to construct the control law with distributed characteristics of the system,so that the output of the multi-agent system tends to be consistent.With the continuous development and improvement on distributed parameter system theory and multi-agent system theory,the research of control problems based on distributed parameter multi-agent system is more and more essential,and its application for industrial production is also more and more common.Iterative learning control does not require high accuracy of the model,and it can track the model without static error,which is widely used in various industrial processes.In this paper,the problem of iterative learning consensus control for second-order distributed parameter multi-agent systems is considered.The specific works are as follows:(1)PD type iterative learning consensus control for second-order hyperbolic distributed parameter multi-agent systems.For a class of second-order hyperbolic distributed parameters,a PD type iterative learning control law is constructed according to the characteristics of the system;the relationship between the system error and the partial derivative of the system error is obtained by using Gronwall inequality and analysing;the sufficient condition for the consensus of the system output is obtained according to the relationship between the system state vector and the partial derivative of the system error.(2)PI type iterative learning consensus control for second-order hyperbolic distributed parameter multi-agent systems based on finite difference method.Aiming at a class of second-order hyperbolic distributed parameter multi-agent system,the discrete format of the system and the corresponding discrete format of the control law are given through analysis;the vector group of system tracking error and state is defined,and we can obtain the new connection that along the value between the double iterative system output difference and the tracking error is obtained;according to the iterative convergence principle and the difference between the two iterative outputs of the system,the sufficient condition for the uniform convergence of the system error is obtained.(3)Second order P-type iterative learning consensus control for hyperbolic distributed parameter multi-agent systems with time delay.For a class of systems with state delay,a second-order iterative learning consensus control scheme is proposed based on the network topology and the nearest neighbor knowledge.For the proposed controller,a discrete-time dynamic system with respect to the number of iterations is constructed,and the stability problem of the discrete-time dynamic system is from the consensus problem of the initial system.With the help of Gronwall inequality,any two parameters are obtained.A sufficient condition for uniform error convergence between agents.