Data-Driven Stochastic Optimal Iterative Learning Control for Nonlinear Non-Affine Systems With Measurement Data Loss

Hao Liang,Yunkai Lv,Yumei Sun,Ronghu Chi,Debin Kong

doi:10.1109/access.2019.2941514

Hao Liang, Yunkai Lv + Show 3 more

Open Access

https://doi.org/10.1109/access.2019.2941514

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Abstract

In this paper, the measurement data loss is considered and two data-driven stochastic optimal iterative learning control (DDSOILC) methods are presented directly for nonlinear network systems. Specifically, an iterative dynamic linearization (IDL) is adopted to construct the linear incremental input output relationship of the repetitive nonlinear network system between two consecutive iterations. In the sequel, a lifted IDL is obtained by defining two super vectors of inputs and outputs over the entire finite time interval. Then, a lifted IDL-based DDSOILC scheme is proposed where the random data loss is described by a Bernoulli distribution of random variable. The results are extended by using a non-lifted IDL where the input-output relationship is described pointwisely. The learning gains of the proposed two methods are iteration-time-variant and can be iteratively estimated using real-time data. The proposed two methods do not depend on any explicit model. Moreover, the proposed non-lifted IDL-based DDSOILC can use more control information than the proposed lifted IDL-based one, and thus it can achieve a better control performance. Both theoretical analysis and simulations verify the efficiency and applicability of the two proposed methods.

Highlights

Iterative learning control (ILC) [1] is most effective to attain a perfect convergence in a finite operation length for repetitive
Inspired by the above discussion, two data-driven stochastic optimal ILC (DDSOILC) approaches are proposed in this work for a general nonlinear nonaffine discrete-time system with random data loss
The main contributions of this article can be given as: (a) The designed learning control laws have nonlinear P-type structures and the learning gain varies with both time and iteration directions and can be estimated iteratively through the proposed parameter updating law; (b) The proposed data-driven stochastic optimal iterative learning control (DDSOILC) methods are data-driven, where no explicit model information is involved in the control system analysis and synthesis except for the input and output data only; (c) The DDSOILC based on non-lifted iterative dynamic linearization (IDL) outperforms the DDSOILC based on lifted IDL because it takes advantage of much more control information obtained in previous time instants at each batch

Summary

INTRODUCTION

Iterative learning control (ILC) [1] is most effective to attain a perfect convergence in a finite operation length for repetitive. A robust ILC design and analysis have been provided in [20] for a nonlinear affine plant with random data loss. Inspired by the above discussion, two data-driven stochastic optimal ILC (DDSOILC) approaches are proposed in this work for a general nonlinear nonaffine discrete-time system with random data loss. (a) The designed learning control laws have nonlinear P-type structures and the learning gain varies with both time and iteration directions and can be estimated iteratively through the proposed parameter updating law; (b) The proposed DDSOILC methods are data-driven, where no explicit model information is involved in the control system analysis and synthesis except for the input and output data only; (c) The DDSOILC based on non-lifted IDL outperforms the DDSOILC based on lifted IDL because it takes advantage of much more control information obtained in previous time instants at each batch.

REVIEW OF ITERATIVE DYNAMICAL LINEARIZATION

CONVERGENCE ANALYSIS

CONTROLLER DESIGN

SIMULATION STUDY

CONCLUSION