2D学习增益自适应调整的离散时间非线性系统迭代学习控制

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"这篇研究论文提出了一种新颖的基于二维学习增益自适应调整的离散时间非线性系统的迭代学习控制方法。该方法适用于一类一般的单输入单输出（SISO）离散时间非线性系统。通过在迭代域内对受控非线性系统的一种等效紧凑型动态线性化数据模型，设计了迭代学习律，利用递归搜索算法自适应地调整二维学习增益，仅需受控非线性系统的测量输入/输出数据。理论分析证明了提出的迭代学习控制能确保跟踪误差的收敛性。此外，通过一个具有时变结构、阶次和参数的复杂未知非线性系统的仿真验证了所提方法的有效性。" 本文的核心知识点包括： 1. **迭代学习控制（Iterative Learning Control, ILC）**：ILC是一种控制策略，通过反复执行任务来改善系统性能，每次迭代都基于前一次的经验进行调整，以减少错误或提高精度。在本研究中，ILC被应用于离散时间非线性系统。 2. **二维学习增益（2D Learning Gain）**：学习增益是ILC中用于调整控制信号的一个参数，它决定了每次迭代中学习速度的快慢。二维学习增益意味着有两个独立的增益参数，可能分别对应时间和状态的不同维度，以实现更精细的控制。 3. **自适应调谐**：通过递归搜索算法，系统能够根据实际运行数据动态调整二维学习增益，使得控制性能得到优化，无需事先完全了解系统的动态特性。 4. **离散时间非线性系统**：与连续时间系统相对，离散时间系统在时间上是不连续的，数据采样间隔固定。非线性系统则包含非线性函数，其输出不仅仅与输入成比例关系，处理这类系统通常需要特殊的控制策略。 5. **等效紧凑型动态线性化数据模型**：这是一种数学建模方法，将非线性系统在迭代域内转化为线性模型，便于应用线性控制理论进行分析和设计。 6. **跟踪误差收敛性**：理论分析证明了所提出的ILC方法可以保证跟踪误差随迭代次数增加而收敛到零，这意味着系统性能会逐渐接近理想目标。 7. **仿真验证**：通过模拟一个具有时变特性的复杂未知非线性系统，作者展示了所提控制策略的实际效果，进一步确认了其有效性和适应性。这篇研究论文提出了一个新的迭代学习控制方法，它利用自适应调谐的二维学习增益来优化对离散时间非线性系统的控制，特别是在只有输入输出数据的情况下。这种方法的理论保证和实际应用潜力对于非线性控制领域具有重要意义。

Iterative Learning Control for Discrete-Time Nonlinear Systems

Based on Adaptive Tuning of 2D Learning Gain

Xian Yu, Zhongsheng Hou

∗

, Chenkun Yin

Advanced Control Systems Laboratory, School of Electronics and Information Engineering, Beijing Jiaotong University, Beijing 100044,

P. R. China

E-mail: 15111013@bjtu.edu.cn, zhshhou@bjtu.edu.cn, chkyin@bjtu.edu.cn

Abstract: A novel data-driven iterative learning control (ILC) based on the adaptive tuning of the 2D learning gain, is proposed

in this paper for a class of general discrete-time nonlinear SISO systems. Based on an equivalent compact form dynamic lin-

earization data model of the controlled nonlinear system in the iteration domain, an iterative learning law is formulated by using

a recursive search algorithm to adaptively tune the 2D learning gain with only the requirement of the measured I/O data of the

controlled nonlinear system. The theoretical analysis shows that the proposed ILC guarantees convergence of the tracking error.

The effectiveness of the proposed ILC is validated by simulations on a complex unknown nonlinear system with time-varying

structure, order and parameters.

Key Words: Iterative Learning Control, Compact Form Dynamic Linearization, Recursive Search Algorithm, Discrete-Time

Nonlinear System

1 Introduction

With a task of achieving perfect tracking from trial to tri-

al in a ﬁnite duration, iterative learning control (ILC) is a

unique and effective control strategy. Since the ﬁrst intro-

duction of this method [1] for robot applications, there have

been widespread studies on ILC over the past 30 years and

prominent progress has been made in both theory and appli-

cations. By taking advantage of the information from previ-

ous iterations, an iterative learning law in a simple structure

can guarantee high performance with smal transient tracking

error for both linear and nonlinear systems.

ILC has been extensively applied in different ﬁelds of

repetitive systems such as freeway trafﬁc [2], robotics [3, 4],

inverted pendulums [5], electromechanical benchmarking

test facilities [6], artiﬁcial pancreatic

-Cell [7] etc. The

design processes of many above mentioned are based on the

model of the controlled plants and they are primarily focused

on linear systems. However, the complexity of production

processes is an increasing obstacle for modeling the con-

trolled plants with the ﬁrst principles or identiﬁcation meth-

ods, and it makes the model-based ILC time-consuming, in-

efﬁcient even inapplicable in some circumstances.

Facing the challenges brought by the modeling, a nov-

el kind of ILC methods called model-free or data-driven

ILC, with few priori model information of the controlled

plants, have attracted increasing attention [1, 8–15]. Most

of the data-driven ILC methods use ﬁxed learning gain,

which makes them inﬂexible especially in the circum-

stances of varying factors, such as iteration-varying trajec-

tory, iteration-varying unknown parameters and iteration-

varying disturbances [13]. Different from the ﬁxed learning

gain controller, another kinds of controller design technique

based on certain equivalent model or some function approx-

imation of the controlled plants has been proposed and ap-

plied in practice, such as the terminal point linear dynamics

over the iteration axis of an original system [11], the Fourier

series approximation [14] and the fuzzy basis approximation

This work is supported by National Natural Science Foundation (NNS-

F) of China under Grants 61433002 and 61403025.

[5] and the wavelet basis approximation [15].

Model free adaptive control (MFAC) was ﬁrst proposed

for a class of discrete-time nonlinear systems [16], which can

equivalently transform to dynamic linearization data models,

using technique such as the compact form dynamic lineariza-

tion (CFDL), the partial form dynamic linearization (PFDL)

and the full form dynamic linearization (FFDL). Inspired by

the dynamic linearization technique, a novel data-driven IL-

C approach is proposed in this paper for a class of gener-

al discrete-time nonlinear single-input-single-output (SISO)

systems and the corresponding convergence analysis is giv-

en.

The main features of the ILC approach proposed in this

paper, comparing with the most ILC methods existing in the

current literatures, are presented as follows. Based on an

equivalent compact form dynamic linearization data model

of the controlled plant in the iteration domain, the model of

the controlled plant is not involved in the controller design.

A 2D learning gain is proposed in this paper and adaptive-

ly tuned by utilizing a recursive search algorithm with only

the requirement of the measured I/O data of the controlled

plant. Besides, with the adaptive tuning of the 2D learning

gain, the proposed ILC approach could be applied to the cir-

cumstances with iteration-varying reference trajectory and

nonidentical initial condition, and its effectiveness is validat-

ed by simulations on a complex unknown nonlinear system

with time-varying structure, order and parameters.

This paper is arranged as follows. An equivalent com-

pact form dynamic linearization technique for the original

controlled plant and the 2D learning gain are described in

Section 2. Section 3 introduces the design and convergence

analysis of the controlled plant. Some simulations are shown

in Section 4 to verify the validity of the ILC approach pro-

posed in this paper. Section 5 is the conclusion.

2 Problem Formulation

2.1 CFDL for Nonlinear Systems

A repeatable discrete-time nonlinear SISO system is con-

sidered as follows

Proceedings of the 36th Chinese Control Conference

Jul

26-28, 2017, Dalian, China

3581

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