Observer Based Distributed Fault Detection And Fault Estimation For Multi-Agent Systems

In the modern industrial system,the controlled systems become much more complex.Thus,the traditional centralized control strategy is difficult to meet the comprehensive requirements of production control.In order to solve the control problems of complex large-scale system,more and more scholars have paid attention to multi-agent systems.Based on the cooperation of different agents,multi-agent systems can achieve specific complex control objectives.Compared with the centralized system,multi-agent systems have higher design flexibility and stronger robustness.In the real production process,as time progresses and environment changes,the fault is inevitable in multi-agent systems because of the large scale systems and complex network structure construction.Because of the communication between agents,the fault information of one agent may pass to their neighbor agents and even spread to the entire network.In some cases,the fault in some key nodes may destroy the whole systems.Because of the information interactions among different agents,the traditional centralized fault detection and fault estimation methods are difficult to be extended directly to distributed multi-agent systems.Therefore,there are great theoretical and practical significance to consider the problems of fault detection and fault estimation for multi-agent systems.Under this background,this dissertation is devoted to distributed fault detection and fault estimation problems for multi-agent systems.Firstly,for the case that the observer matching condition is satisfied,the distributed fault detection observers are designed for linear and nonlinear multi-agent systems,respectively.Furthermore,the distributed fault detection problem for multi-agent systems is investigated under the condition that the observer matching condition is not satisfied.Then,based on the measurement output information of the agents,the design schemes of reduced order fault detection observer and the fault detection observer with adjustable dimension are studied.Finally,the method of fault estimation is given for a class of nonlinear multi-agent systems.Specifically,the main contributions of this dissertation include the following aspects:1)The distributed fault detection problem for a class of continuous-time linear multi-agent systems with unknown input is considered.By constructing unknown input observer in one agent,the fault in its specified neighbor can be detected.Two types of observers are designed.The proposed methods can be applied to the case that there is more than one faulty agent in the systems.The unknown input is decoupled from the residual.The observer parameter matrices can be calculated by solving the linear matrix inequality and a set of matrix equations.Two simulation examples are given to illustrate the effectiveness of the proposed methods.2)The problem of fault detection for a class of nonlinear high order heterogeneous multi-agent systems is studied.The nonlinear part of the multi-agent systems can be divided into two parts:the known Lipschitz nonlinear function and the unknown nonlinear function.By designing unknown input observers in an agent,the fault in its neighbor nodes can be detected.According to the number of the neighbor nodes,two fault detection methods are proposed.Compared with existing methods,the proposed methods have a wider application range.In the observer design process,the unknown nonlinear part(including disturbance,uncertainty,etc.)does not appear in the residual dynamic,which ensures the robustness of the fault detection residual to the unknown input.Three examples are provided to demonstrate the effectiveness of the proposed methods.3)The fault detection problem for a class of higher order linear multi-agent systems with disturbance is considered.In order to detect the fault in one agent,the faults in other agents and the disturbance in the systems are treated as unknown input,then the unknown input observer is designed in its neighbor node.It is assumed that the observer matching condition is not satisfied,i.e.,the unknown input can not be decoupled from the fault detection residual.For this case,the unknown input is decomposed into two parts.One part can be decoupled from the residual,and the other part cannot be decoupled from the residual.By designing the robust fault detection observer,the effect of one part unknown input can be removed from the residual,and the effect of the other unknown input is constrained by the H performance index.Hence,the residual is robust to the unknown input.Finally,two simulation examples are given to demonstrate the effectiveness of the proposed method.4)For linear multi-agent systems,the reduced order observer based distributed fault detection problem is investigated.The unknown input observers are constructed in one agent to detect the possible faults in its neighbor nodes.In the observer design process,the measurement output of the agent,in which the observer is designed,and its neighbors are used.By selecting a proper coordinate transformation,the multi-agent systems can be decomposed into two subsystems,the state of one subsystem is the measurement output of the agent,in which the observer is designed,and its neighbors.Furthermore,the fault detection observer is designed to estimate the system state of the other subsystem.The cases that the observer matching condition is satisfied and is not satisfied are considered.Compared with existing results,the total dimension of the designed observers is greatly reduced.Finally,two simulation examples are provided to illustrate the effectiveness of the proposed methods.5)For a class of nonlinear multi-agent systems,a new fault detection observer design method is proposed.By designing nonlinear unknown input observers in one agent,the faults in its neighbor nodes can be detected.In the observer design process,the states and the differential of the output of the agent,in which the observers are designed,and its neighbor agents are not needed.Compared with existing results,the dimension of the designed observers can be adjusted freely in a certain range,thus the tradeoff between detection results and the detection cost can be achieved.By solving the linear matrix inequality and matrix equations,the parameter matrices of the observer can be easily computed.In addition,in the process of observer design,some parameter matrices can be selected freely.This implies that more design freedoms can be obtained.Finally,simulation examples are given to demonstrate the effectiveness of the proposed method.6)For a class of continuous-time nonlinear multi-agent systems,based on the fault estimation observer,the method of distributed fault estimation is proposed.By designing an observer in one agent,the faults in itself and its neighbor nodes can be estimated.In the design process of the fault estimation observer,only the output of the agent,in which the observer is designed,and its neighbor agents are needed.Besides,the designed observer can estimate the states of the corresponding agents.By choosing the region pole constraint,we can adjust the rate of convergence of the estimation error system and improve the estimation performance.Finally,simulation example is given to demonstrate the effectiveness of the proposed method.