Iterative learning control for strictly unknown nonlinear systems subject to external disturbances

Abstract

This paper deals with Iterative Learning Control ILC schemes to solve the trajectory tracking problem of strictly unknown nonlinear systems subject to external disturbances, and performing repetitive tasks. Two ILC laws are presented, the first law is the high order, i.e., the information (error) of several iterations are used in the control law. The second law is the ILC with forgetting factor, i.e., the control of the preceding iteration is multiplied by a matrix of the gains. Indeed, the advantage of these algorithms, it is not only applicable for nonlinear systems with model uncertainty, but also for nonlinear systems with no data exists, neither in the structure model nor in the system parameters. In addition, the control design is very simple in the sense that there is no requirement on the choice of the learning gains. Furthermore, the convergence of our algorithms is independent of initial conditions. The asymptotic stability of the closed loop system is guaranteed. This proof is based upon the use of a Lyapunov-like positive definite sequence, which is shown to be monotonically decreasing under the proposed control schemes. Finally, simulation results on nonlinear system are provided to illustrate the effectiveness of the proposed controllers.

High-Order Feedback Iterative Learning Control Algorithm with Forgetting Factor

“…When conditions V = 0 and ‖ (0)‖ = 0 are satisfied, from (17), we get = 0 and from (19), we obtain lim → ∞ ‖ ‖ = 0. Then, (16) gives lim → ∞ ‖ ‖ = 0; we have lim → ∞ ‖ ( )‖ = lim → ∞ ‖ ‖ = 0.…”

“…If̃≤ ∑ =1̃< 1, then lim → ∞ ≤̃/(1 −̃). By Lemma 3, we choose a sufficiently large constant such that the following inequality holds when conditions̃< 1 and = ∑ =1 < 1 are satisfied: (16), (17), and (19), we get that the tracking error bound converges to a small neighborhood of the origin, as goes to infinity. Meanwhile, the tracking error ‖ ‖ , initial state error ‖ (0)‖ , and the bound of output disturbance item V have a linear relationship.…”

“…The contribution of this paper is a combination of the high-order feedback iterative learning control and forgetting factor. Through a new ILC algorithm, the perfect tracking control performance of the robot manipulators can be achieved in the repetitive nonlinear time-varying systems [17,18] with uncertainty and disturbance [19,20]. A rigorous proof based on the Lipschitz-like approach is given to guarantee the stability and convergence of nonlinear system.…”

High Order Feedback-Feedforward Iterative Learning Control Scheme with a Variable Forgetting Factor

“…Let us consider repetitive non-linear time-varying systems [16][17] with uncertainty and disturbances [18][19]: …”

Adaptive P‐type iterative learning radial basis function control for robot manipulators with unknown varying disturbances and unknown input dead zone

“…Over the last two decades, this technique has been the center of interest of many researchers. [2][3][4][5][6][7][8][9][10][11][12][13][14][15] dead-zone may severely degrade system performance. How to deal with these uncertainties becomes another direction in the development of ILC.…”