Adaptive Fault-tolerant Control For High-order Nonlinear Systems With Actuator Failures

In recent years,with the industrial process getting much more large-scale and complex,the status of equipment in production appears vital in particular and the requirements for control quality are becoming increasingly high,precise and accurate.In the production process,once the physical components of control system such as actuator,sensor and other components become faulty,it will lead to system running unstable.Then the control result is inconsistent with the expected objective and it is more likely to cause the huge personnel or economic losses.For the sake of guaranteeing the safety and reliability of modern complex systems,many domestic and international scholars have devoted themselves to the research of fault-tolerant control for nonlinear systems.Due to the complexity of the theoretical research for high-order nonlinear systems,little fault-tolerant researches have been done on this system at present.As a result,the fault-tolerant control for more complex high-order nonlinear systems deserves more research.This paper focuses on the issue of fault-tolerant control for high-order nonlinear systems.By effectively combining backstepping control,command filter,adaptive control and supervisory controller,the corresponding fault-tolerant control scheme is investigated for high-order nonlinear systems with actuator faults.This paper mainly addresses the following points:Firstly,the fault tolerant control problem is investigated for a class of high-order nonlinear systems.By using the approximation capability of the neural networks,an adaptive fault tolerant control scheme is proposed.Based on Lyapunov stability theory,all of the signals in the closed-loop system are proved to be semi-globally uniformly ultimately bounded.Simulation results show the validity of the design approach.Secondly,the problem of adaptive fault tolerant control is investigated for a class of high-order strict-feedback nonlinear systems with the actuator bias fault,and an adaptive backstepping fault tolerant control strategy is proposed in this paper.Compared with the traditional first-order strict-feedback nonlinear systems,high-order strict-feedback nonlinear systems are more general,but more difficult to handle.In particular,this system occurs actuator failure,which generates the additional terms in the controller design process.To address the unknown nonlinearities in the system,neural networks are introduced to approximate the unknown continuous nonlinear functions.Based on Lyapunov stability theory,it is proved that the tracking error converges to a small adjustable neighborhood of the origin with all signals in the closed-loop system being bounded.Finally,the simulation results demonstrate the effectiveness of the control strategy.Thirdly,the problem of adaptive fault-tolerant tracking control is investigated for a class of nonlinear high-order strict-feedback systems with actuator fault,and a new command-filter-based adaptive neural supervisory backstepping control strategy is proposed,where command filters are applied to overcome the so-called "explosion of complexity" occurred in conventional backstepping technique and to remove the condition that the first n derivatives of tracking reference signal should be known.Note that,from function approximation theory,for an unknown smooth function,only if its variables always belong to a set,it can be approximated by neural networks.In the backstepping control strategy,supervisory control is applied to ensure that all the variables at each step belong to a compact set and to further ensure that the unknown function derived at each step can be approximated by neural networks,which guarantees the strictness of the theoretical analysis and overcomes some the shortcomings in the existing results of backstepping control.Finally,the effectiveness of the design scheme is verified by the simulation results.