This paper addresses the vibration control and the input constraint for an Euler-Bernoulli beam system under aperiodic distributed disturbance and aperiodic boundary disturbance. Hyperbolic tangent functions and saturation functions are adopted to tackle the input constraint. A restrained adaptive boundary iterative learning control (ABILC) law is proposed based on a time-weighted Lyapunov-Krasovskii-like composite energy function. In order to deal with the uncertainty of a system parameter and reject the external disturbances, three adaptive laws are designed and learned in the iteration domain. All the system states of the closed-loop system are proved to be bounded in each iteration. Along the iteration axis, the displacements asymptotically converge toward zero. Simulation results are provided to illustrate the effectiveness of the proposed ABILC scheme.
In this work, sampled-data iterative learning control (ILC) method is extended to a class of continuous-time nonlinear systems with iteration-varying trial lengths.In order to propose a unified ILC algorithm, the tracking errors will be redefined when the trial length is shorter or longer than the desired one. Based on the modified tracking errors, 2 sampled-data ILC schemes are proposed to handle the randomly varying trial lengths. Sufficient conditions are derived rigorously to guarantee the convergence of the nonlinear system at each sampling instant.To verify the effectiveness of the proposed ILC laws, simulations for a nonlinear system are performed. The simulation results show that if the sampling period is set to be small enough, the convergence of the learning algorithms can be achieved as the iteration number increases.
KEYWORDSinitial state condition, iteration learning control, iteration-varying lengths, iteratively moving average operator, relative degree, sampled-data Int J Robust Nonlinear Control. 2018;28:3073-3091.wileyonlinelibrary.com/journal/rnc
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