Iterative Learning Control With Varying Trial Lengths Based On Composite Energy Function

Iterative learning control(ILC),an important branch of the field of intelligent control,is especially suitable for those systems that can perform a specific task over a fixed time interval and repeat the same operation.Using the experience of previous batches to update the control input,the control performance of the system is gradually improved along with the increase of iterative trials.To gradually improve the tracking performance along the iteration axis,ILC requires operation lengths to be consistent.However,in practical applications,this condition is violated due to complex factors and unknown uncertainties.There were some pioneering studies trying to resolve this problem,but most of them considered discrete-time linear systems and few papers have considered continuous-time nonlinear systems.In consideration of this finding,this paper studies continuous-time nonlinear systems with iteration-varying trial lengths.Main contributions are as follows:Chapter 2 studies ILC for parametric nonlinear systems with iteration-varying lengths.With partial structure information,two ILC schemes are proposed.When unknown parameters can be separated as time-varying and time-invariant parts,a difference-differential mixing scheme is proposed.When unknown parameters are time-invariant,a difference-differential hybrid adaptive law is presented,which can also handle certain time-varying uncertainty in parameters.Two compensation mechanisms for the missing tracking error are given in this chapter,and a new composite energy function(CEF)is introduced.The convergence of proposed algorithms is strictly proven.Chapter 3 studies ILC for manipulator systems with iteration-varying lengths.A virtual tracking error is defined in this chapter,and a CEF is constructed based on the auxiliary variable to prove convergence of joint position tracking errors.In addition,considering the random initial state issue,an initial rectifying mechanism is introduced to ensure accurate tracking performance of the joint position beyond a small initial time interval.Chapter 4 studies ILC for high-order strict-feedback nonlinear systems with unknown control direction under iteration-varying length environments.A neural network is introduced to approximate unmodeled nonlinear dynamics,and a differential learning algorithm is designed to estimate unknown weights of the neural network.With the compensated virtual tracking error,a CEF is constructed to analyze the convergence of the proposed control algorithm.