Robust Adaptive Iterative Learning Consensus For Uncertain Multi-agent Systems

Through the information exchange and collaboration of each agent in the multi-agent system,the multi-agent system can solve the complex tasks that single agent unable to complete.Coordinated control problem of multi-agent system has been highly applied in many fields such as industrial field and formation control.The consensus problem of multi-agent system plays an important role in the coordination field.The adaptive iterative learning control strategy can guarantee the convergence performance of the consensus error for multi-agent system in the finite time interval,it can also eliminate the uncertainties in the system effectively at the same time.At present,there are a few results of applying the adaptive iterative learning control strategy to multi-agent system.In this paper,we investigate the exactly consensus and formation control problem of first-order and high-order multi-agent systems with uncertain communication topology structure and high-order multi-agent systems with unknown time-iteration-varying parameters.And the corresponding distributed robust adaptive iterative learning control protocols are proposed under the condition that only a portion of the follower agents have access to the information of the leader and the initial state error exists.Finally,sufficient conditions of exact consensus for the multi-agent system in the finite time interval are obtained by Lyapunov theory analysis under initial-state learning condition.The main results of the paper are organized as follows:For the first-order parameterized nonlinear multi-agent system with uncertain communication topology structure.Firstly,we use T-S fuzzy models to approximate the uncertain topological structure of multi-agent system.Without using any global information,a new robust adaptive iterative learning control law is designed based on the fuzzy general consensus error under initial-state learning condition.The proposed distributed control law can ensure all the follower agents of the multi-agent system track the leader exactly in the finite time interval,and the proposed control law is also applicable to the formation control of multi-agent systems.Based on the effective approximation characteristic of T-S fuzzy model with the uncertain nonlinear mapping and structure,we extend the results to the high-order parameterized multi-agent systems with uncertain topological structure.The robust adaptive iterative learning control law is designed based on the filtered error under the initial-state learning condition.And the sufficient condition for the exact convergence of the consensus error of the high-order multi-agent system is obtained through the Lyapunov theory analysis.The proposed control law can also solve the formation problem of the multi-agent system effectively.For the high-order multi-agent system with unknown time-iteration-varying parameters,a high-order internal model is used to model the unknown iteration-varying parameters.Then we propose a new HOIM-based robust adaptive iterative learning control law to deal with the consensus tracking problem for multi-agent system under the alignment condition.Finally,the sufficient condition for the exactly consensus result of the multi-agent system is obtained through the strict proof of the composite energy function.Similarly,we also give the formation control results of multi-agent systems.