Research On Finite-time Cooperative Control Of Disturbed Multi-agent Systems

Many phenomena in nature and many systems in engineering applications can be modeled or discribed by multi-agent systems.Cooperative control is a very important topic for multi-agent systems.At the same time,for cooperative control,consensus problem is the foundation.Both in theoretical analysis and practical engineering design and application,the methods it use can trace back to the consensus control method.With the in-depth study of multi-agent system control,various control algorithms which satisfying different application conditions continue to be put forward,and the consensus theory is becoming more and more perfect.However,the main results of the traditional research tend to be asymptotical convergence.In some applications,engineers hope to get finite-time convergence or fixed-time convergence algorithm.In this paper,based on the finite-time control method of the conventional single system control,the finite-time or fixed-time control algorithm in multi-agent systems is given and improved.In the results of the existing multi-agent system control problems,the model is mainly aimed to deal with the ideal model,that is,the disturbance term and the uncertain part of the system model are not considered in each agent.Some results are concerned with these problems,but are obtained under the results of asymptotical convergence.In the past several years,many researchers have paid close attention to finite-time or fixed-time anti-disturbance control of multi-agent systems.In this paper,based on the super-twisting sliding mode control method,the finite-time stability or fixed-time stability is given under the condition of considering system disturbance.The structure of this paper is arranged as follows.In the first chapter,we summarize the research background of multi-agent anti-disturbance control methods and the research status at China and abroad.The common methods of anti-disturbance control are introduced,and the basic framework and design idea are given.In the second chapter,from the perspective of theoretical basis,we introduce the relevant theoretical contents of the former results in the form of theorems.They mainly include algebraic graph theory,Lyapunov stability theory,finite-time stability theory,sliding mode control method and disturbance observer method.In the third chapter,we study the application of super-twisting control method in the finite-time consensus of multi-agent systems.The relevant theoretical proof is given.The main task is to design the variable-gain super-twisting control algorithm.Through a single system variable-gain super-twisting control method and a framework based on Lyapunov function,a detailed design method is given.In this chapter,the conventional first-order sliding mode control method,the second-order sliding mode control method and the variable-gain second-order sliding mode control method are also simulated and compared in the application of multi-agent systems.In the fourth chapter,a fixed-time consensus method based on disturbance observer for multi-agent systems is studied.By constructing a fixed-time convergent disturbance observer and virtual speed design,the common second-order multi-agent system can achieve fixed-time consensus.In addition,matching and mismatching disturbances both exist in the second-order multi-agent system model.The simulation results show that the controller design is effective.This chapter is the center of the thesis.In the fifth chapter,we studied the tracking control problem of second order disturbed multi-agent systems.For a reference system with given dynamic and unknown inputs,a tracking controller and a state observer are designed based on the method in Chapter 4,so that each agent can track the state of reference system at a fixed time.The sixth chapter gives a summary of the work and prospects for the future work.