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                    含未知動態與擾動的非線性系統神經網絡嵌入學習控制

                    馬樂 閆一鳴 徐東甫 李志偉 孫靈芳

                    馬樂,  閆一鳴,  徐東甫,  李志偉,  孫靈芳.  含未知動態與擾動的非線性系統神經網絡嵌入學習控制.  自動化學報,  2021,  47(8): 2016?2028 doi: 10.16383/j.aas.c200186
                    引用本文: 馬樂,  閆一鳴,  徐東甫,  李志偉,  孫靈芳.  含未知動態與擾動的非線性系統神經網絡嵌入學習控制.  自動化學報,  2021,  47(8): 2016?2028 doi: 10.16383/j.aas.c200186
                    Ma Le,  Yan Yi-Ming,  Xu Dong-Fu,  Li Zhi-Wei,  Sun Ling-Fang.  Neural network embedded learning control for nonlinear system with unknown dynamics and disturbance.  Acta Automatica Sinica,  2021,  47(8): 2016?2028 doi: 10.16383/j.aas.c200186
                    Citation: Ma Le,  Yan Yi-Ming,  Xu Dong-Fu,  Li Zhi-Wei,  Sun Ling-Fang.  Neural network embedded learning control for nonlinear system with unknown dynamics and disturbance.  Acta Automatica Sinica,  2021,  47(8): 2016?2028 doi: 10.16383/j.aas.c200186

                    含未知動態與擾動的非線性系統神經網絡嵌入學習控制

                    doi: 10.16383/j.aas.c200186
                    基金項目: 國家自然科學基金(61673101)資助;吉林重點行業與產業科技創新計劃人工智能專項(2019001090)
                    詳細信息
                      作者簡介:

                      馬樂:東北電力大學自動化工程學院副教授. 主要研究方向為機器人學習、控制與視覺.E-mail: male_robot_nedu@sina.com

                      閆一鳴:東北電力大學自動化工程學院碩士研究生. 主要研究方向為神經網絡學習控制. E-mail: ddyym3914@163.com

                      徐東甫:東北電力大學自動化工程學院副教授. 主要研究方向為機器人導航與控制. 本文通信作者.E-mail: xu.dong.fu@163.com

                      李志偉:東北電力大學自動化工程學院副教授. 主要研究方向為非線性系統建模、控制及數值模擬. E-mail: zhiwei.li@neepu.edu.cn

                      孫靈芳:東北電力大學自動化工程學院教授. 主要研究方向為熱工過程先進控制. E-mail: 15043283452@163.com

                    • 收稿日期 2020-04-06 錄用日期 2020-07-21 Manuscript received April 6, 2020; accepted July 21, 2020 國家自然科學基金 (61673101), 吉林重點行業與產業科技創新計劃人工智能專項 (2019001090) 資助 Supported by National Natural Science Foundation of China (61673101), Special Foundation for Artificial Intelligence in Innovative Project of Science and Technology Key Industries of Jilin (2019001090) 本文責任編委 王占山
                    • Recommended by Associate Editor WANG Zhan-Shan 1. 東北電力大學自動化工程學院 吉林 132012 2. 吉林省精密驅動智能控制國際聯合研究中心 吉林 132012 1. School of Automation and Engineering, Northeast Electric Power University, Jilin 132012 2. Jilin Province International Research Center of Precision Drive and Intelligent Control, Jilin 132012

                    Neural Network Embedded Learning Control for Nonlinear System With Unknown Dynamics and Disturbance

                    Funds: Supported by National Natural Science Foundation of China (61673101), pecial Foundation for Artificial Intelligence in Innovative project of Science and Technology Key Industries of Jilin (2019001090)
                    More Information
                      Author Bio:

                      MA Le Associate professor at the School of Automation and Engineering, Northeast Electric Power University. His main research interest is robotics learning, controlling and vision

                      YAN Yi-Ming Master student at the School of Automation and Engineering, Northeast Electric Power University. His main research interest is neural network learning control

                      XU Dong-Fu Associate professor at the School of Automation and Engineering, Northeast Electric Power University. His main research interest is robot navigation and control. Corresponding author of this paper

                      LI Zhi-Wei Associate professor at the School of Automation and Engineering, Northeast Electric Power University. His main research interest is modeling, control and numerical simulation of nonlinear system

                      SUN Ling-Fang Professor at the School of Automation and Engineering, Northeast Electric Power University. His main research interest is advanced control of thermal process

                    • 摘要:

                      針對帶有不確定性與擾動的非線性系統的性能優化問題, 提出一種基于神經網絡嵌入的學習控制方法. 對一類常見的 Lyapunov 函數導數形式, 將神經網絡控制器集成到某種對系統穩定的基準控制器中, 其意義在于將原控制器改進為滿足Lyapunov穩定的神經網絡參數可調控制器, 從而能夠利用先進的神經網絡學習技術實現控制器的在線優化. 建立了跟蹤誤差的等效目標函數, 避免了對系統輸入–輸出的辨識問題. 建立了一種未知非線性與擾動等效值自適應方法, 并依此方法設計基準控制器. 以RBF (Radial basis function) 反步自適應控制、基于卷積神經網絡的滑??刂坪蜕疃葟娀瘜W習控制為對比方法, 對帶有死區、飽和、三角函數等數值與物理非線性模型進行仿真分析以測試方法有效性, 并針對上肢康復機器人控制問題進行虛擬實驗以驗證該方法的實用性. 仿真與實驗結果表明, 該方法能在Lyapunov 穩定條件下有效優化基礎控制器性能, 對比結果證實了該方法的實用性與先進性.

                      1)  收稿日期 2020-04-06 錄用日期 2020-07-21 Manuscript received April 6, 2020; accepted July 21, 2020 國家自然科學基金 (61673101), 吉林重點行業與產業科技創新計劃人工智能專項 (2019001090) 資助 Supported by National Natural Science Foundation of China (61673101), Special Foundation for Artificial Intelligence in Innovative Project of Science and Technology Key Industries of Jilin (2019001090) 本文責任編委 王占山
                      2)  Recommended by Associate Editor WANG Zhan-Shan 1. 東北電力大學自動化工程學院 吉林 132012 2. 吉林省精密驅動智能控制國際聯合研究中心 吉林 132012 1. School of Automation and Engineering, Northeast Electric Power University, Jilin 132012 2. Jilin Province International Research Center of Precision Drive and Intelligent Control, Jilin 132012
                    • 圖  1  算例1控制性能結果

                      Fig.  1  The controllers performances of the Example 1

                      圖  2  算例2控制性能結果

                      Fig.  2  The controllers performances of the Example 2

                      圖  3  算例3控制性能結果

                      Fig.  3  The controllers performances of the Example 3

                      圖  4  算例4對比實驗控制性能結果

                      Fig.  4  The results for comparison test of control performances of the Example 4

                      圖  5  CoppeliaSim虛擬實驗示意圖

                      Fig.  5  The demonstration of virtual experiment in CoppeliaSim

                      圖  6  不同體重康復者測試跟蹤誤差與控制輸入MAE

                      Fig.  6  The MAE of tracking errors and control inputs for tests to rehabilitation clients with different weights

                      圖  7  不同康復任務測試跟蹤誤差與控制輸入MAE

                      Fig.  7  The MAE of tracking errors and control inputs for tests to different rehabilitation tasks

                      圖  8  帶有康復者關節擾動的機器人控制對比實驗結果

                      Fig.  8  Comparison results of robot control methods for joint disturbances created by rehabilitation client

                      A1  算例1 ~ 3與5.1節、5.2節學習控制器神經網絡結構

                      A1  The architecture of neural network of learning controller in exmples 1 ~ 3 and subsection 5.1 ~ 5.2

                      A2  算例4學習控制器神經網絡結構

                      A2  The architecture of neural network of learning controller in the example 4

                      表  1  算例4兩種方法控制性能統計數據對比

                      Table  1  The comparison for control statistical indicators of two methods in the Example 4

                      方法 $\max|e|$ ${\rm{mean}}|e|$ $\max|u|$
                      文獻 [13] 0.1350 0.0360 83.6962
                      本文 0.0788 0.0210 81.4951
                      方法 ${\rm{mean}}|u|$ $\max|\tilde{{\cal{F}}}|$ ${\rm{mean}}|\tilde{{\cal{F}}}|$
                      文獻 [13] 7.6009 15.8421 5.1999
                      本文 7.7972 14.0492 4.6208
                      下載: 導出CSV

                      B1  ?

                      第 1 節變量與符號 說明
                      $ {\cal{S}} $ $ n $階$ m $維狀態反饋系統
                      $ {\boldsymbol{F}} $ 未知非線性函數向量
                      $ {\boldsymbol{d}} $ 有界未知擾動向量
                      $ {\boldsymbol} $ $ m $階未知可逆對角常數矩陣
                      $ V $, $ \dot{V} $ Lyapunov 函數及其導數
                      $ {\cal{B}} $, $ {\cal{M}} $ $ \dot{V} $中已知函數向量
                      ${{\varphi} }$ $ \dot{V} $中不含$ {\boldsymbol{u}} $的其余項之和
                      $ {\boldsymbol{u}}_{{\rm}} $ 基礎控制器
                      $ {\boldsymbol{\mu}}( \cdot | {\boldsymbol{\theta}}) $ 神經網絡嵌入控制器
                      $ {\boldsymbol{u}}_{{\rm}}^{{\boldsymbol{\mu}}} $ 基于$ {\boldsymbol{u}}_{{\rm}} $與$ {\boldsymbol{\mu}}( \cdot | {\boldsymbol{\theta}}) $的學習控制器
                      $ \circ $ Hadamard 積運算符
                      $ {\boldsymbol{\vartheta}}(\cdot) $ 嵌入控制器約束函數向量
                      $ {\cal{L}} $ 系統控制性能的量度
                      下載: 導出CSV

                      B2  ?

                      第 2 ~ 3 節變量與符號 說明
                      $ {\cal{L}}_{{\cal{S}}} $ 系統$ {\cal{S}} $的性能優化目標函數
                      $ \psi $ $ {\cal{L}}_{{\cal{S}}} $中其他控制指標正則項
                      $ {\boldsymbol}_{0} $ $ m $階已知對角常值矩陣
                      $ {\cal{F}} $, $ \dot{{\cal{F}}} $ 不確定與擾動值項的等效值與導數
                      $ \hat{{\cal{F}}} $, $ \dot{\hat{{\cal{F}}}} $ $ {\cal{F}} $的估計值及其導數
                      $ \tilde{{\cal{F}}} $, $ \dot{\tilde{{\cal{F}}}} $ $ {\cal{F}} $與$ \hat{{\cal{F}}} $的誤差及其導數
                      $ {\boldsymbol{u}}_{{\rm}}^{{\cal{F}}} $ 基于值自適應的基礎控制器
                      ${\boldsymbol{\varpi}}(\cdot)$ 構造$ {\boldsymbol{u}}_{{\rm}}^{{\cal{F}}} $所需函數
                      下載: 導出CSV

                      B3  ?

                      第 4 ~ 5 節變量與符號 說明
                      $ y_{{\rm{d}}} $ 系統期望輸出
                      $ b_{0} $ 已知系統增益 ($ {\boldsymbol}_{0} $的一維形式)
                      $ \hat{f} $ 待估計不確定項
                      $ k $ 控制器增益
                      $ \xi(t) $ 隨機變量
                      $ \theta $, $ \omega $ 電機角度與角速度
                      $ f_{{\rm{M}}} $ 電機模型未知非線性項
                      $ \theta_{{\rm{J}}} $, $ \omega_{{\rm{J}}} $ 機械臂關節角度與角速度
                      $ \gamma $ DRL 方法的獎勵函數
                      下載: 導出CSV
                      360彩票
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                    • 收稿日期:  2020-04-06
                    • 錄用日期:  2020-07-22
                    • 網絡出版日期:  2021-08-25
                    • 刊出日期:  2021-08-20

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