Design Of Sparse Fault-tolerant Controllers For Distributed Networked Control Systems

Networked control systems(NCSs)are closed-loop systems that connect plants,controllers,sensors and actuators through shared network.Its system structure is huge and complicated,and the possibility of failure of each component is large.If some actuators,sensors or other components fail,the conventional feedback control may degrade the system performance or even lead to the collapse of the whole system.Therefore,it is necessary to give a method that can guarantee the system performance in the case of the failures.In recent years,due to the demands of modern control work,the distributed control of large-scale interconnected systems has also received widespread attention.In a distributed networked control system,each subsystem transmits its state information through the connected channels between controllers,and the information transmitted determines the convergence and stability of the whole system.However,in the current research,the problem of connected channels failure is rarely considered,and there are a large number of actuators and sensors in the system,so the fault is inevitable.Therefore,it is of great significance to study the fault-tolerant control of distributed networked systems.The main work of this paper is as follows:(1)For a class of event-triggered networked control systems,the number of fault actuators is constrained,the contribution is to convert the number of fault actuators to a cardinality constraints on the row of the controller gain matrix.The mixed integer programming is used to solve this kind of sparse constraints problem,this method uses a 0-1 variable to add appropriate constraints to the controller gain matrix,that makes the maximum absolute value of a row element in the matrix is zero,so as to get the zero rows,and the number of zero rows in the gain matrix means the number of system fault actuators.By using the Lyapunov functional method and matrix transformation,we obtained a sufficient condition for the system to be H? exponentially asymptotically stable with a limited number of actuator failures and a controller design method with row sparse constraints is also presented.Finally,the effectiveness of the proposed method is verified by two simulation examples.(2)For a class of distributed networked control systems,the number of fault sensors is constrained,the contribution is to convert the number of fault sensors to a cardinality constraints on the column of the distributed controller gain matrix.This kind of fault-tolerant control problem with sparse constraints is solved by mixed integer programming method.By using the Lyapunov functional and linear matrix inequalities method,we obtained a sufficient condition for the system to satisfy H? stability and a distributed controller design method with column sparse constraints is also presented.Finally,the effectiveness of the proposed method is verified by a numerical example.(3)For a class of event-triggered distributed networked control systems,the number of fault connected channels is constrained,the contribution is to convert the number of fault connected channels to a cardinality constraints on the zero-block of the connection matrix.In the same way,the mixed integer programming is used to solve this kind of sparse constraints problem.By using the Lyapunov functional and linear matrix inequalities method,we obtained a sufficient condition for the system to be H? asymptotically stable and a distributed controller design method with sparse connected channels fault is also presented.Finally,the effectiveness of the proposed method is verified by two simulation examples.