Adaptive Iterative Learning Control of Non-uniform Trajectory Tracking for Strict Feedback Nonlinear Time-varying Systems

Abstract

In this paper, an iterative learning control strategy is presented for a class of nonlinear time-varying systems, the timevarying parameters are expanded into Fourier series with bounded remainder term. The backstepping design technique is used to deal with system dynamics with non-global Lipschitz nonlinearities and the approach proposed in this paper solves the non-uniform trajectory tracking problem. Based on the Lyapunov-like synthesis, the proposed method shows that all signals in the closed-loop system remain bounded over a pre-specified time interval [0, T ]. And perfect non-uniform trajectory tracking of the system output is completed. A typical series is introduced in order to deal with the unknown bound of remainder term. Finally, a simulation example shows the feasibility and effectiveness of the approach.

Non-uniform Trajectory Tracking AILC for Nonlinear Time-varying Parameter System with Multiple Unknown Control Directions

“…The controller design adopts the quadratic obstacle Lyapunov function, so that the tank gun control system has excellent track performance. An non-uniform target tracking AILC method was proposed in the paper [11]. The paper [12] proposed a fault-tolerant ILC technique for mobile robots non-repetitive target tracking with output constraints.…”

Adaptive iterative learning control for unknown linear time-varying continuous systems

“…Where these parameters are unknown time-varying and system performs a defined task in a finite time interval, and hence we encounter with an unknown time-varying repetitive system. The controller design for such systems becomes a challenging topic (Zhang and Li, 2014). Even though so far, various procedures are presented to control unknown nonlinear repetitive systems in the both time-invariant and time-variant cases (for example, one can refer to Bensidhoum et al, 2019; Bu et al, 2018; Chi et al, 2015; Chien and Liu, 1996; Ghotb Razmjou et al, 2018; Li and Hu, 2012; Liang et al, 2019; Ouyang, 2011; Xu and Xu, 2004; Yu and Li, 2017; Yin et al, 2010), but because intrinsic complexity of these procedures that are merely for nonlinear repetitive systems, do not seem to be an engineering task and to be justifiable using these procedures for linear cases.…”

Fourier Series Learning Control for Torque Ripple Minimization in Permanent Magnet Synchronous Motors

“…In piezoelectrically-actuated systems, this approach can estimate the system dynamics and uncertainties on-line, and no prior knowledge of system dynamics is required [24,25]. An adaptive iterative learning controller can be designed for nonlinear systems with unknown time-varying parameters to realize the non-uniform trajectory tracking perfectly when the time varying parameters are expanded into Fourier series with bounded remainder terms [26].…”