非线性不确定系统准最优学习控制

严求真; 孙明轩

doi:10.16383/j.aas.2015.c140781

非线性不确定系统准最优学习控制

doi: 10.16383/j.aas.2015.c140781

严求真^1,2,
孙明轩^1, ,

1.
浙江工业大学信息工程学院杭州 310023;
2.
浙江水利水电学院信息工程学院杭州 310018

基金项目:

国家自然科学基金(60874041,61174034,61374103),浙江省高等学校访问学者专业发展项目(FX2013206)资助

详细信息

作者简介:
严求真浙江工业大学信息工程学院博士研究生.主要研究方向为学习控制.E-mail:zjyqz@126.com

通讯作者:
孙明轩浙江工业大学信息工程学院教授.主要研究方向为学习控制.本文通信作者.E-mail:mxsun@zjut.edu.cn

计量
- 文章访问数: 1736
- HTML全文浏览量: 100
- PDF下载量: 1314
- 被引次数: 22
出版历程
- 收稿日期: 2014-11-13
- 修回日期: 2015-03-03
- 刊出日期: 2015-09-20

Suboptimal Learning Control for Nonlinear Systems with Both Parametric and Nonparametric Uncertainties

YAN Qiu-Zhen^1,2,
SUN Ming-Xuan^{1
, ,}

1.
College of Information Engineering, Zhejiang University of Technology, Hangzhou 310023;
2.
College of Information Engineering, Zhejiang University of Water Resources and Electric Power, Hangzhou 310018

Funds:

Supported by National Natural Science Foundation of China (60874041, 61174034, 61374103) and University Visiting Scholars Developing Project of Zhejiang Province (FX2013206)

摘要

摘要: 针对不确定非线性系统, 提出准最优学习控制方法, 解决参数与非参数不确定特性同时存在情形下的轨迹跟踪问题. 给出迭代学习与重复学习两种控制策略, 根据Sontag公式解决标称系统的优化控制, 并以鲁棒学习手段处理参数与非参数不确定特性. 提出断续函数连续化方案, 以避免传统Sontag公式在实现时可能存在的颤振问题. 分析证明经过足够多次迭代或足够多个周期的重复运行后, 闭环系统可实现系统状态以预设精度跟踪参考信号. 仿真结果表明所设计学习系统在收敛速度方面快于非优化设计.
- 准最优非线性控制 /
- 学习控制 /
- 参数化 /
- 非参数不确定性
Abstract: In this paper, two suboptimal learning control methods, an iterative one and a repetitive one, are proposed for a class of nonlinear systems with both time-varying parametric and nonparametric uncertainties. Sontag formula is used for the control design of a nominal system, while the robust learning mechanism is adopted to deal with both parametric and nonparametric uncertainties. A continuous controller design is carried out in order to avoid the chattering phenomenon that may arise due to the use of Sontag formula. It is shown that the closed-loop system state follows the desired trajectory with the pre-specified accuracy, as iteration or repetition increases. Numerical results demonstrate the effectiveness of the suboptimal learning control scheme.
- Suboptimal nonlinear control /
- learning control /
- parametrization /
- nonparametric uncertainties

HTML全文

参考文献(24)

[1]	Arimoto S, Kawamura S, Miyazaki F. Bettering operation of robots by learning. Journal of Robotic Systems, 1984, 1(2): 123-140
[2]	Dixon W E, Zergeroglu E, Dawson D M, Costic B T. Repetitive learning control: a Lyapunov-based approach. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 2002, 32(4): 538-545
[3]	Xu J X, Tan Y. A composite energy function-based learning control approach for nonlinear systems with time-varying parametric uncertainties. IEEE Transactions on Automatic Control, 2002, 47(11): 1940-1945
[4]	Chen Wei-Sheng, Wang Yuan-Liang, Li Jun-Min. Adaptive learning control for nonlinearly parameterized systems with periodically time-varying delays. Acta Automatica Sinica, 2008, 34(12): 1556-1560 (陈为胜, 王元亮, 李俊民. 周期时变时滞非线性参数化系统的自适应学习控制. 自动化学报, 2008, 34(12): 1556-1560)
[5]	Yin C K, Xu J X, Hou Z S. A high-order internal model based iterative learning control scheme for nonlinear systems with time-iteration-varying parameters. IEEE Transactions on Automatic Control, 2010, 55(11): 2665-2670
[6]	Tayebi A. Adaptive iterative learning control for robot manipulators. Automatica, 2004, 40(7): 1195-1203
[7]	Xu J X, Xu J. On iterative learning from different tracking tasks in the presence of time-varying uncertainties. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics, 2004, 34(1): 589-597
[8]	Ham C, Qu Z H. A new learning control based on the Lyapunov direct method. In: Proceedings of Southcon/94 Conference Record. Orlando, FL: IEEE, 1994. 121-125
[9]	Jin X, Xu J X. Iterative learning control for output-constrained systems with both parametric and nonparametric uncertainties. Automatica, 2013, 49(8): 2508-2516
[10]	Chen Peng-Nian, Qin Hua-Shu. Adaptive tracking control of periodic signals for a class of uncertain nonlinear systems. Journal of Systems Science and Mathematical Sciences, 2009, 29(10): 1343-1352 (陈彭年, 秦化淑. 不确定非线性系统的周期信号自适应跟踪. 系统科学与数学, 2009, 29(10): 1343-1352)
[11]	Marino R, Tomei P, Verrelli C M. Robust adaptive learning control for nonlinear systems with extended matching unstructured uncertainties. International Journal of Robust and Nonlinear Control, 2012, 22(6): 645-675
[12]	Anderson B D O, Moore J B. Optimal Control: Linear Quadratic Methods. Englewood Cliffs, NJ: Prentice-Hall, 1990.
[13]	Xu J X, Tan Y. A suboptimal learning control scheme for non-linear systems with time-varying parametric uncertainties. Optimal Control Applications and Methods, 2001, 22(3): 111-126
[14]	Sontag E D. A Lyapunov-like characterization of asymptotic controllability. SIAM Journal of Control and Optimization, 1989, 21(3): 462-471
[15]	Chen Yi-Mei, Han Zheng-Zhi. Optimal adaptive control of a class of nonlinear uncertain systems. Acta Automatica Sinica, 2006, 32(1): 54-59 (陈奕梅, 韩正之. 一类非线性不确定系统的最优自适应控制. 自动化学报, 2006, 32(1): 54-59)
[16]	Chien C J, Hsu C T, Yao C Y. Fuzzy system-based adaptive iterative learning control for nonlinear plants with initial state errors. IEEE Transactions on Fuzzy Systems, 2004, 12(5): 724-732
[17]	Yan Qiu-Zhen, Sun Ming-Xuan. Error trajectory tracking by robust learning control for nonlinear systems. Control Theory & Applications, 2013, 30(1): 23-30 (严求真, 孙明轩. 一类非线性系统的误差轨迹跟踪鲁棒学习控制算法. 控制理论与应用, 2013, 30(1): 23-30)
[18]	Lv Qing, Fang Yong-Chun, Ren Xiao. Iterative learning control for accelerated inhibition effect of initial state random error. Acta Automatica Sinica, 2014, 40(7): 1295-1302 (吕庆, 方勇纯, 任逍. 加速抑制随机初态误差影响的迭代学习控制. 自动化学报, 2014, 40(7): 1295-1302)
[19]	Sun M X, Wang D W, Chen P N. Repetitive learning control of nonlinear systems over finite intervals. Science in China Series F: Information Sciences, 2010, 53(1): 115-128
[20]	Xu J X, Qu Z H. Robust iterative learning control for a class of nonlinear systems. Automatica, 1998, 34(8): 983-988
[21]	Xu Xin, Shen Dong, Gao Yan-Qing, Wang Kai. Learning control of dynamical systems based on Markov decision processes: research frontiers and outlooks. Acta Automatica Sinica, 2012, 38(5): 673-687 (徐昕, 沈栋, 高岩青, 王凯. 基于马氏决策过程模型的动态系统学习控制: 研究前沿与展望. 自动化学报, 2012, 38(5): 673-687)
[22]	Zhang Li, Liu Shan. Basis function based adaptive iterative learning control for non-minimum phase systems. Acta Automatica Sinica, 2014, 40(12): 2716-2725 (张黎, 刘山. 非最小相位系统的基函数型自适应迭代学习控制. 自动化学报, 2014, 40(12): 2716-2725)
[23]	Sepulchre R, Jankovic M, Kokotovic P V. Constructive Nonlinear Control. New York: Springer, 1997.
[24]	Xu J X. A quasi-optimal sliding mode control scheme based on control Lyapunov function. Journal of the Franklin Institute, 2012, 349(4): 1445-1458

施引文献

期刊类型引用(12)

1.	朱亚文，周红标，李杨，徐浩渊. 约束多目标进化算法研究进展. 计算机应用研究. 2022(09): 2582-2590+2602 . 百度学术
2.	潘子肖，雷德明. 基于问题性质的分布式低碳并行机调度算法研究. 自动化学报. 2020(11): 2427-2438 . 本站查看
3.	王学武，魏建斌，周昕，顾幸生. 一种基于超体积指标的多目标进化算法. 华东理工大学学报(自然科学版). 2020(06): 780-791 . 百度学术
4.	张海瑞. 基于LLE降维方法的Pareto优劣性预测. 湖南理工学院学报(自然科学版). 2018(03): 30-35 . 百度学术
5.	余梓. PCA下的地铁工程项目多目标集成管理分析. 科技资讯. 2018(04): 87-88 . 百度学术
6.	陈志旺，黄兴旺，陈志兴，赵子铮，黄丽芳. 区间多目标优化非支配排序云模型算法. 计算机工程与应用. 2017(22): 143-149 . 百度学术
7.	闫红. 基于区间可信度下界的多目标优化算法研究及应用. 计算机科学. 2017(S2): 577-579+585 . 百度学术
8.	陈志旺，赵子铮，姚嘉楠，韩艳. 昂贵区间多目标优化空间数据挖掘求解策略. 控制与决策. 2017(09): 1599-1606 . 百度学术
9.	李文彬，贺建军，冯彩英，郭观七. 基于决策空间变换最近邻方法的Pareto支配性预测. 自动化学报. 2017(02): 294-301 . 本站查看
10.	王晓原，张敬磊，刘振雪，尹超. 基于混合模糊多人多目标非合作博弈的车道选择模型. 自动化学报. 2017(11): 2033-2043 . 本站查看
11.	陈志旺，黄兴旺，陈志兴，赵子铮. 融合高斯建模和近邻法的区间多目标支配性预测策略. 小型微型计算机系统. 2017(08): 1806-1810 . 百度学术
12.	丁进良，杨翠娥，陈立鹏，柴天佑. 基于参考点预测的动态多目标优化算法. 自动化学报. 2017(02): 313-320 . 本站查看