A New AILC for a Class of Nonlinearly Parameterized Systems with Unknown Delays and Input Dead-Zone

Abstract

This paper presents an adaptive iterative learning control (AILC) scheme for a class of nonlinear systems with unknown time-varying delays and unknown input dead-zone. A novel nonlinear form of deadzone nonlinearity is presented. The assumption of identical initial condition for ILC is removed by introducing boundary layer functions. The uncertainties with time-varying delays are compensated for with assistance of appropriate Lyapunov-Krasovskii functional and Young’s inequality. The hyperbolic tangent function is employed to avoid the possible singularity problem. According to a property of hyperbolic tangent function, the system output is proved to converge to a small neighborhood of the desired trajectory by constructing Lyapunov-like composite energy function (CEF) in two cases, while maintaining all the closed-loop signals bounded. Finally, a simulation example is presented to verify the effectiveness of the proposed approach.

Observer-Based Adaptive Iterative Learning Control for a Class of Nonlinear Time Delay Systems with Input Saturation

“…Consequently, stabilization problem of control systems with time delay has received much attention for several decades and a large number of research results have been reported in the literature that deal with various analysis and design problems [11][12][13][14][15][16]. However, in the field of AILC, only a few results are available for nonlinear systems with time delays [17][18][19]. In [17], an AILC strategy was developed for a class of scalar systems with unknown time-varying delay and then extended to a class of high-order systems with both time-varying and time-invariant parameters, where the unknown time-varying parameter was estimated in the iterative learning process.…”

“…However, the proposed controller in [17] requires that the uncertainties in the system satisfy local Lipschitz condition and nonlinear parameterized condition such that adaptive learning laws can be used to estimate the unknown timevarying parameters. In [18,19], we designed an AILC scheme for a class of nonlinearly parameterized systems and an RBF NN-based AILC for class of unparameterized systems, respectively, where the systems in two papers are with both unknown time-varying delays and unknown dead zone input. However, all of the aforementioned results are on systems with time delay states.…”

The Effect of Initial State Error for Nonlinear Systems with Delay via Iterative Learning Control

“…Stabilization problem of control systems with delay has received much attention for several decades and some research results have been reported in the literature (see [3,11,13,[15][16][17][18][19][20][21][22][23]). However, only a few results are available for nonlinear systems, combining with the iterative learning control items, with time delays [11,[24][25][26]. In this paper, under the case that the th iterative state vector ( ) is different from the ( +1)th iterative state vector +1 ( ), that is, +1 ( ) − ( ) ̸ = 0, the iterative learning controller of nonlinear time-delayed systems is designed by using -norm and retarded Gronwall-like inequality.…”

“…Theorem 6. For system (25) and a given reference ( ), if conditions (9) are true and there exist matrix and functions ,ℎ ( ) and ,ℎ ( ) such that ∫ 0 ,ℎ ( ) = 1, > ℎ, ‖ ‖ is bounded, max(‖ − 1 ‖, ‖ − 2 ‖) ≤ < 1, where is a constant, then system (25) with the iterative learning control law can guarantee that lim →∞ ( ) = ( ) is bounded but ( ) cannot track ( ) on ∈ [0, ℎ] and lim →∞ ( ) = ( ) on ∈ [ℎ, ] for arbitrary initial state (0).…”