ILC for Non-Linear Hyperbolic Partial Difference Systems

Abstract

This paper discusses the iterative learning control problem for a class of non-linear partial difference system hyperbolic types. The proposed algorithm is the PD-type iterative learning control algorithm with initial state learning. Initially, we introduced the hyperbolic system and the control law used. Subsequently, we presented some dilemmas. Then, sufficient conditions for monotone convergence of the tracking error are established under the convenient assumption. Furthermore, we give a detailed convergence analysis based on previously given lemmas and the discrete Gronwall’s inequality for the system. Finally, we illustrate the effectiveness of the method using a numerical example.

Iterative learning control for time-delay non-linear DPS hyperbolic type

“…According to the Proposition 1, Lemma 1, and because ||e k (., 0)|| L 2 → 0 when k → ∞ we get ||e k (., 1)|| L 2 → 0 when k → ∞ For more details see [18] Theorem 1 Suppose that Proposition 1 and Assumption 1 are satisfied. If…”

“…After Arimoto introduced the theory of iterative learning control in 1984, the research of ILC has become a subject of focus in the field of controllers, conducive research advancement has been made in theory and application. ILC has been used to track a determined target in many systems [13,11,12] including distributed parameter systems or partial differential systems [14,15], partial difference systems [16][17][18], and the delay systems [19][20][21][22][23][24][25]. In [19], the authors considerers the PD-type iterative learning control method for a class of nonlinear time-delay systems.…”

“…From the emphasis overhead, here in this paper, we study the ILC problem of varying time-delay nonlinear distributed parameter systems. Because of the system complexity in this work, the discrete form (partial difference system [18])is used. The proposed technique is an ILC algorithm based on the PD-controller and a new output function for the system.…”

“…1. Because of the method's high performance with the nonlinear hyperbolic partial difference systems [18], here, an extension of the technique to a class of nonlinear hyperbolic DPS with varying time delay is given, where the sufficient condition of the convergence are provided in the iteration domain. 2.…”