Adaptive ILC of Tracking Nonrepetitive Trajectory for Two-dimensional Nonlinear Discrete Time-varying Fornasini-Marchesi
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ISSN:1598-6446 eISSN:2005-4092 http://www.springer.com/12555
Adaptive ILC of Tracking Nonrepetitive Trajectory for Two-dimensional Nonlinear Discrete Time-varying Fornasini-Marchesini Systems with Iteration-varying Boundary States Kai Wan and Yun-Shan Wei* Abstract: Most of adaptive iterative learning control (AILC) algorithms focus on one-dimensional (1-D) systems, rather than two-dimensional (2-D) systems. This brief is first concerned with AILC for 2-D nonlinear discrete timevarying Fornasini-Marchesini system (NDTVFMS) with nonrepetitive reference trajectory under iteration-varying boundary states. By using Lyapunov analysis method, it can guarantee that the ultimate tracking error tends to zero asymptotically, and make all identified parameters and system signals to be bounded as iteration number goes to infinity. Two illustrative examples are used to validate the effectiveness of the designed AILC approach. Keywords: Adaptive iterative learning control (AILC), iteration-varying boundary states, nonrepetitive reference trajectory, 2-D nonlinear discrete time-varying Fornasini-Marchesini system (2-D NDTVFMS).
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INTRODUCTION
Iterative learning control (ILC) is an unsupervised and data-driven control strategy, which constantly renovates the control input for a class of repetitive dynamical systems that carry out a given task over a fixed time interval. The information of error and control input in the preceding trial is applied to renovate a new control input in the next trial, such that the tracking performance of plants is greatly improved. ILC techniques presented in the controlled system community, such as stochastic ILC, adaptive ILC (AILC), and optimal ILC, are prevalent in practical industrious processing control. A general introduction to ILC design and research based on the methodology the contraction mapping and can be found in [1]. However, most of the ILC approaches unavoidably suffer from a lot of problems mainly refer to iteration-invariant reference trajectory, reset condition. In [2, 3], there have existed some basic assumptions and limitations. Combined with adaptive control technique and ILC techniques, a new AILC approach based on Lyapunov stability theory is introduced to solve these issues. AILC technique has contributed greatly in dealing with the nonrepetitive trajectory tracking or the issue of iteration-varying initial error [4–10]. However, a great many of existing AILC
research results which hitherto chiefly concentrated on one-dimensional (1-D) systems. Due to wide existence in many practical applications, such as multi-dimensional robotic manipulators [11], image data processing [12] and 2-D dynamical networks [13]. Based on the background of these applications of 2-D dynamical systems, which promotes us to build a broad engineering blueprint for ILC theories, and make it a rigorous and promising branch in scientific research. Unfortunately, few researches for ILC have extended to 2-D systems because of their complicated model structure. ILC approaches for 2-D systems was introd
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