Researches On Fault-Tolerant And Robust Control Of Time-Delay Systems

With the development of modern science technology,the function of the system is more and more perfect,and the complexity of the system is more and more high,which make the influence of time delay,uncertainty,fault and so on,on the system inevitable in the control process.If the influence cannot be managed and controlled timely,it may result in the system performance degradation,instability,out-of-operation,even huge losses.Therefore,in order to improve the reliability,robustness and security of the time-delay systems,fault-tolerant control and robust control have been received more attention in the research on control theory.Based on Lyapunov stability method and LMI technique,fault-tolerant control and robust H? performance analysis axe investigated for the time-delay systems in this paper,and a series of theoretical results are obtained.Meanwhile,these theories are proved to be feasible by applying them into the practical systems.In order to effectively reduce the conservativeness of the proposed methods,Jensen inequality,Wirtinger inequality,convex combination technique,rcciprocally convex combination technique and event-driven method are mainly used in this paper.The main work of this paper are given as follows:(1)For a class of system with time delay and disturbance,the method of designing an adaptive reliable H? fault-tolerant controller is addressed.In the case of the existence of actuator faults in the system,in order to reflect the influence of the disturbances and time delays on the system simultaneously,the defi-nition of the improved H? performance indexes are proposed.On the basis of the online estimates of actuator faults,the adaptive controller parameters are updated automatically to compensate the influence of the faults on the system,while making sure the satisfactory adaptive H? performance indexes in fault-free case and fault case for the closed-loop system.By choosing suit-able Lyapunov function,the sufficient conditions of asymptotic stability are obtained.Compared with the stability condition obtained by the fixed gain controller,the stability condition obtained by the adaptive controller not only has simple structure,but also is less conservative.(2)Based on the improved H? performance index proposed in the previous chap-ter,the method of designing an adaptive reliable H? fault-tolerant controller with quantized feedback is addressed for the system with time delay and dis-turbance.On the basis of online estimates of actuator faults,the controller parameters are updated automatically to compensate the influence of the faults on the system,while ensuring the desired improved H? performance preserved.The Lyapunov function candidate is constructed to prove that the closed-loop system is asymptotically stable.And the existing sufficient conditions of the controller are proved to be less conservative.The gains of the controller and the parameters of the adaptive law are co-designed and obtained in terms of solutions to a set of LMIs.(3)For the state-dependent uncertainty systems,the design problems of the observer-based event-driven robust H? controllers are investigated.Based on the state-dependent state observer,the event-driven criterion is proposed to determine whether the newly sampled states should be sent out to the con-troller.As a result,the communication resources can be saved significantly,and the burden of the network communication can be reduced.The observer error closed-loop system with the event-driven controller is rewritten as the time-delay system.By choosing the state-dependent integral function to be the Lyapunov function candidate,the less conservative asymptotic stability conditions are obtained,and the desired H? performance of the system are preserved.The observer gain matrix,the controller gain matrix and the event-driven parameters are co-designed and co-obtained in terms of solution to a set of LMIs.(4)On the basis of the state observer,the method of designing an event-driven observer-based fault-tolerant controller is addressed for the state-dependent uncertainty system with external disturbance and fault.Based on the state of the Luenberger-type state-dependent observer,the event-driven criterion is proposed to determine whether the sampled states should be sent out to the controller.As a result,communication resources can be saved significantly,and the network bandwidth can be saved.The observer error closed-loop system is rewritten as the time-delay system.By employing the state-dependent integral function to be the Lyapunov function candidate,the error system is proved to be asymptotically stable,while the desired performance is preserved in the case of the existence of fault.The observer gain,the controller gain and the event-driven parameters can be co-obtained in terms of solution to a set of LMIs.(5)The design problem of an observer-based event-driven robust H? controller with multi-gain is investigated for the state-dependent uncertainty system with time delay.I In the network control system,the event generator is positioned between the sensor and the controller to determine whether the sampled states should be sent out to the controller.As a result,communication resources can be saved significantly and the usage of network bandwidth can be reduced.The closed-loop system with the state observer and the event-driven controller is rewritten as the multi-time-delay system.Based on Wirtinger-based integral inequality and reciprocally convex combination inequality,the conditions of the asymptotical stability analysis and control synthesis are established in terms of LMIs for the closed-loop system.(6)In the sense of input-to-state stability(ISS),an event-driven robust H? con-troller is designed for the state-dependent uncertainty system.By Lyapunov function method,linear matrix inequality(LMI)technique and Wirtinger-based integral inequality technique,the sufficient conditions of ISS are de-veloped for the state-dependent uncertainty system.In the sense of ISS,the event-driven criterion is proposed by the energy at previous release time and the value of the K-function ?(·)at current time in this paper.The event-driven controller and the event-driven criterion can be co-designed by the proposed method.The relationship among the controller,the criterion and the ISS conditions is described by a set of LMIs.Finally,the full text work are summarized.Some unsolved problems and de-velopment directions for fault tolerant control and robust control of the time-delay systems are proposed.Furthermore,the prospects of the further study are given.