离散系统迭代学习型瞬时最优控制及作动器位置优化研究

童少伟; 唐怀平

doi:10.3879/j.issn.1000-0887.2016.02.005

离散系统迭代学习型瞬时最优控制及作动器位置优化研究

doi: 10.3879/j.issn.1000-0887.2016.02.005

西南交通大学力学与工程学院, 成都 610031

基金项目: 国家自然科学基金（51378437）

详细信息

作者简介:
童少伟（1985—），男，博士生(通讯作者. E-mail: wt900800@126.com).

中图分类号: P315.9
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- 被引次数: 0
出版历程
- 收稿日期: 2015-07-08
- 修回日期: 2015-12-08
- 刊出日期: 2016-02-15

Iterative Learning Instantaneous Optimal Control of Discrete Systems and Optimization

School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, P.R.China

Funds: The National Natural Science Foundation of China(51378437)

摘要

摘要: 以线性离散系统为研究对象，以瞬时最优化控制和智能算法中的迭代学习控制为基础，以系统响应期望值与实际值之差为反馈信号，以离散系统的二次型性能泛函为目标函数，提出了迭代学习型瞬时最优控制算法.该方法以瞬时最优化控制算法初始化控制信号，并采用迭代学习控制在线实时修正控制信号以提高主动控制的效果.针对迭代学习型瞬时最优化控制算法迭代的特性，采用范数方法给出了该算法收敛的充分条件.数值算例表明，迭代学习型瞬时最优控制算法较离散瞬时最优控制算法有较明显的优势.同时，基于改进遗传算法，对主动控制器位置优化进行了讨论.数值分析结果表明：部分楼层设置主动控制器且安装位置经过优化后，其控制效果可接近甚至优于全楼层设置主动控制器时的控制效果.
- 瞬时最优控制 /
- 迭代学习控制 /
- 稳定性 /
- 性能泛函 /
- 遗传算法
Abstract: Through combination of the instantaneous optimal control (IOC) and the iterative learning control (ILC), one new hybrid control strategy called the iterative learning instantaneous optimal control was proposed. The discrete linear system was chosen as the target model for the new control strategy, and the quadratic performance functional of the discrete system was taken as the objective function to be minimized. During the controlling process of the system, the core idea of the ILC was introduced in order to modify the control signals which were initialized by the IOC. With the method of matrix norms, the sufficient condition for convergence of the new control strategy was established. Compared with the IOC, the iterative learning instantaneous optimal control gives simulation results of improved effectiveness. Furthermore, based on the improved genetic algorithm (GA), the optimization of the actuator positions in a multistory building to be controlled was investigated. Results of the numerical simulation indicate that, while the actuators are partially positioned at some optimally seleted floors, the control effects may reach or even be better than those in the case of full installation of actuators at all floors.
- instantaneous optimal control /
- iterative learning control /
- stability /
- performance functional /
- genetic algorithm

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参考文献(16)

[1]	Yang J N, Akbarpour A, Ghaemmaghami P. Optimal control algorithms for earthquake-excited buildings[C]//Proceeding of 2nd International Symposium on Structural Control,1985.
[2]	Yang J N, Akbarpour A, Ghaemmaghami P. New optimal control algorithms for structural control[J].Journal of Engineering Mechanics,1987,113(9): 1369-1386.
[3]	Yang J N, Li Z, Liu S C. Stable controllers for instantaneous optimal control[J].Journal of Engineering Mechanics,1992,118(8): 1612-1630.
[4]	Bahar O, Mahzoon M, Bann M R, Kitagawa Y. Discrete instantaneous optimal control method[J].Iranian Journal of Science & Technology,2004,28(B1): 9-20.
[5]	杨飏, 寇捷. 基于能量法的结构瞬时最优控制的参数影响[J]. 东北大学学报(自然科学版), 2011,32(9): 1356-1359.(YANG Yang, KOU Jie. Parameter effect of the instantaneous optimal control based on the energy equation method[J].Journal of Northeastern University(Natural Science),2011,32(9): 1356-1359.(in Chinese）)
[6]	童少伟, 杨翊仁, 唐怀平. 改进IOC控制算法及其在结构振动控制中的应用[J]. 四川大学学报（工程科学版）, 2012,44(S2): 27-30.(TONG Shao-wei, YANG Yi-ren, TANG Huai-ping. An improved instantaneous optimal control algorithm and its numerical applications[J].Journal of Sichuan University(Engineering Science Edition),2012,44(S2): 27-30.(in Chinese）)
[7]	Uchiyama M. Formulation of high-speed motion of a mechanical arm by trial[J].Translation of the Society of Instrumentation and Control Engineers,1978,14(6): 706-7l2.
[8]	Arimoto S, Kawamura S, Miyazaki F. Bettering operation of robotics by learning[J].Journal of Robotic Systems,1984,1(2): 123-140.
[9]	WANG You-qing, GAO Fu-rong , Doyle III Francis J. Survey on iterative learning control, repetitive control, and run-to-run control[J].Journal of Process Control,2009,19(10): 1589-1600.
[10]	Smolders K, Volckaert M, Swevers J. Tracking control of nonlinear lumped mechanical continuoustime systems: a model-based iterative learning approach[J].Mechanical Systems and Signal Processing,2008,22(8): 1896-1916.
[11]	Cueli J R, Bordons C. Iterative nonlinear model predictive control stability, robustness and applications[J]. Control Engineering Practice,2008,16(9):1023-1034.
[12]	李俊民, 王元亮, 李新民. 未知时变时滞非线性参数化系统自适应迭代学习控制[J]. 控制理论与应用, 2011,28(6): 861-868.(LI Jun-min, WANG Yuan-liang, LI Xin-min. Adaptive iterative learning control for nonlinear parameterized-systems with unknown time-varying delays[J].Control Theory & Applications,2011,28(6): 861-868.(in Chinese）)
[13]	曹伟, 丛望, 孙明. 初态学习下时滞非线性系统的迭代学习控制[J]. 仪器仪表学报, 2012,33(2): 315-320.(CAO Wei, CONG Wang, SUN Ming. Iterative learning control with initial state study for nonlinear time-delay system[J].Chinese Journal of Scientific Instrument,2012,33(2): 315-320.(in Chinese）)
[14]	Lynch J P, Law K H. Energy market-based control of linear civil structures[J].Earthquake Engineering and Structural Dynamics,2002,31(10): 1855-1877.
[15]	Zhu T J, Heidebrecht A C, Tso W K. Effect of peak ground acceleration to velocity ratio on the ductility demand of inelastic system[J].Earthquake and Structural Dynamics,1988,16(1): 63-79.
[16]	Elnashai A S, Di Sarno L.Fundamentals of Earthquake Engineering [M]. John Wiley & Sons, Ltd, 2008.