On Learning Control Methods For Uncertain Systems

The common repetitive systems usually perform repetitive control tasks over a finite time interval or track periodically trajectory over an infinite interval.Learning control has been widely used in repetitive systems,due to its structural simplicity and effective learning ability.Learning control includes iterative learning control(ILC)and repetitive learning control(RLC).Based on Lyapunov approach,the learning control methods for uncertain systems are studied.To widen the application field of ILC,and meanwhile improve the security and reliability of the system operation,six aspects of research work are carried out in this dissertation:1.This dissertation studies learning control scheme guaranteeing transient performance bounds,to enhance the safety performance of the system.By introducing an error transformation,the problem of guaranteeing transient performance of the tracking error is converted to that of ensuring boundedness of the transformed error.Applying Lyapunov synthesis,the control design is carried out for handling both parametric and nonparametric uncertainties of system dynamics.It is shown that,with the use of fully-saturated learning mechanisms,the system output could completely track the desired trajectory over the entire pre-specified time interval as iteration increases,and the tracking error is within the transient performance bounds for each iteration cycle,while the boundedness and the uniform convergence of the transformed error are guaranteed.On the basis of the above work,this dissertation proposes an iterative learning control algorithm with guaranteed tracking performance for nonlinear strict-feedback systems.2.For a class of parametric uncertain system under the non-repetitive trajectory,a novel iterative learning control with guaranteed tracking performance is presented.The proposed ILC method overcomes the limitation of traditional ILC in that,both the initial error and the desired trajectory are iteration-varying in the ILC process.A rectified reference signal is constructed,and a polynomial type modifier function is given,which has the advantages of the generality and convenience.Then,the nonzero initial value problem of nonparametric uncertain systems is solved by using the method of constructing the modified reference signal given above.A robust learning controller is designed to deal with the nonparametric uncertainties.It is shown that the system error converges to zero on the specified interval,and the tracking error satisfies the prescribed performance bound for each iteration cycle.3.The problems of fault tolerant iterative learning control for nonlinear systems are studied.A class of MISO system with iteration dependent parametric uncertainty is considered.By applying Backstepping technology and Lyapunov function approach,a novel ILC algorithm is constructed,which can deal with both system uncertainties and actuator failures.On the basis of the above work,an ILC scheme is proposed for nonlinear strict-feedback systems that are subject to actuator faults.An error-tracking approach is used in the analysis to solve the nonzero initial error problem.4.An control scheme to deal with time-varying parametric uncertain problem,is proposed for nonlinear strict-feedback systems performing the repetitive tasks over a finite time interval.A dead-zone modified learning law is used to estimate the bound of the time-varying uncertainties.In order to remove the chattering phenomenon,a novel sign function is constructed by using polynomical function.Based on Backstepping approach and a dead-zone Lyapunov function,ILC algorithm and RLC algorithm are presented respectively.The proposed controller guarantees the boundness of all closedloop signals.It also ensures that the tracking error converges into a prespecified neighborhood.5.For a class of uncertain nonlinear systems,a repetitive learning control approach is designed using the Backstepping method.Based on Lyapunov-like synthesis,a learning controller is designed for handling parametric and nonparametric uncertainties,such that system state can completely track the reference trajectory over the whole time interval after many iterations.Both the partially-saturated and fully-saturated learning mechanisms are discussed respectively.The uniform boundedness of all variables in the closed-loop and the uniform convergence of the tracking error are guaranteed.6.This dissertation presents a finite-time adaptive iterative learning control for robotic systems under arbitrary initial state error.With the concept of initial rectified attractor being introduced,an error variable with an initial rectify term is constructed.The constant robotic system and time-varying robotic system are respectively considered.Based on Lyapunov-like function,accordingly,iterative learning controllers are designed for handling the uncertainties.By applying the unsaturated/ saturated learning mechanisms,the error variable would uniformly converge to zero over the entire time interval as iteration increase,thereby the tracking error would achieve practical complete tracking over a pre-specified interval,while the uniform boundness of all variable in the closed-loop system can be guaranteed.