一类广义大型互联离散时间系统的状态跟踪算法
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摘要
研究一类广义大型互联线性离散时间系统的迭代学习控制问题。借助矩阵奇异值分解,将一类广义大型互联线性离散时间类系统转化为差分代数系统。根据差分代数系统的特性,构建D-P型的学习控制算法。证明在该算法的作用下,系统的状态跟踪误差沿迭代轴方向收敛。最后,数值仿真验证了算法的有效性。
This paper studies the decentralized iterative learning control problem for singular large-scale interconnected linear discrete-time systems. Through decomposing singular matrix, the systems are equivalently resolved into difference-algebraic ones. According to the characteristics of the difference-algebraic systems, the D-P type algorithm is constructed, and by the algorithm, the states of the systems can converge to the desired trajectory accordingly. Finally, a numerical example shows the effectiveness of the proposed algorithm.
This paper studies the decentralized iterative learning control problem for singular large-scale interconnected linear discrete-time systems. Through decomposing singular matrix, the systems are equivalently resolved into difference-algebraic ones. According to the characteristics of the difference-algebraic systems, the D-P type algorithm is constructed, and by the algorithm, the states of the systems can converge to the desired trajectory accordingly. Finally, a numerical example shows the effectiveness of the proposed algorithm.
引文
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[9]田森平,周秀锦.一类广义迭代学习控制系统的状态跟踪算法[J].系统科学与数学,2012,32(6):731-738.
[10]顾盼盼,傅勤,吴健荣.具有固定初始偏移的线性广义迭代学习控制系统的状态跟踪算法[J].应用数学,2017,30(1):8-15.
[11]曹伟,郭媛,孙明.一类离散时间广义系统的迭代学习控制[J].物理学报,2016,65(12):120201-120207.
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[13]傅勤.基于LMI的大型互联线性系统的分散有限时间镇定[J].控制与决策,2010,25(5):763-768.
[14]JAMSHIDI M.Large scale systems:modeling and control[M].North Holland:Elsevier Science Publishing Co.Inc.,1983.
[15]PAGILLA P R,ZHONG H W.Semi-globally stable decentralized control of a class of large-scale interconnected systems[J].Proceedings of the American Control Conference,Denver,Colorado,USA:IEEE,2003,5017-5022.
[16]RUAN X E,BIEN Z,PARK K H.Decentralized iterative learning control to large-scale industrial processes for nonrepetitive trajectory tracking[J].IEEE Transactions on Systems,Man,and Cybernetics-Park A:Systems and Humans,2008,38(1):238-252.
[17]WU H.Decentralized iterative learning control for a class of large scale interconnected dynamical systems[J].Journal of Mathematical Analysis and Applications,2007,327(1):233-245.
[18]FU Q,GU P P,WU J R.Decentralized iterative learning control for large-scale interconnected linear systems with fixed initial shifts[J].International Journal of Control,Automation and Systems,2017,15(5):1991-2000.
[19]张庆灵.广义大系统的分散控制与鲁棒控制[M].西安:西北工业大学出版社,1997.
[20]沃松林,史国栋,邹云.广义大系统的渐进稳定与镇定[J].电机与控制学报,2005,9(3):222-225.
[21]何汉林.数值分析[M].2版.北京:科学出版社,2011.
[2]孙明轩,黄宝健.迭代学习控制[M].北京:国防工业出版社,1999.
[3]谢胜利,田森平,谢振东.迭代学习控制的理论与应用[M].北京:科学出版社,2005.
[4]翟丁,张庆灵,陈晓光,等.广义系统的控制与应用综述[J].计算技术与自动化,2003,22(4):31-36.
[5]DAI L Y.Singular control systems[M].New York:Springer-Verlag,1989.
[6]DUAN G R.Analysis and design of descriptor linear systems[M].Berlin:Springer-Verlag,2010.
[7]王炎,田世昌,孙光伟,等.工业机器人控制[J].自动化技术与应用,1986,5(3):3-10.
[8]朴凤贤,张庆灵.线性广义系统的迭代学习控制[J].控制与决策,2007,22(63):349-356.
[9]田森平,周秀锦.一类广义迭代学习控制系统的状态跟踪算法[J].系统科学与数学,2012,32(6):731-738.
[10]顾盼盼,傅勤,吴健荣.具有固定初始偏移的线性广义迭代学习控制系统的状态跟踪算法[J].应用数学,2017,30(1):8-15.
[11]曹伟,郭媛,孙明.一类离散时间广义系统的迭代学习控制[J].物理学报,2016,65(12):120201-120207.
[12]李向东.几类离散系统的迭代学习控制[D].苏州:苏州科技大学,2017.
[13]傅勤.基于LMI的大型互联线性系统的分散有限时间镇定[J].控制与决策,2010,25(5):763-768.
[14]JAMSHIDI M.Large scale systems:modeling and control[M].North Holland:Elsevier Science Publishing Co.Inc.,1983.
[15]PAGILLA P R,ZHONG H W.Semi-globally stable decentralized control of a class of large-scale interconnected systems[J].Proceedings of the American Control Conference,Denver,Colorado,USA:IEEE,2003,5017-5022.
[16]RUAN X E,BIEN Z,PARK K H.Decentralized iterative learning control to large-scale industrial processes for nonrepetitive trajectory tracking[J].IEEE Transactions on Systems,Man,and Cybernetics-Park A:Systems and Humans,2008,38(1):238-252.
[17]WU H.Decentralized iterative learning control for a class of large scale interconnected dynamical systems[J].Journal of Mathematical Analysis and Applications,2007,327(1):233-245.
[18]FU Q,GU P P,WU J R.Decentralized iterative learning control for large-scale interconnected linear systems with fixed initial shifts[J].International Journal of Control,Automation and Systems,2017,15(5):1991-2000.
[19]张庆灵.广义大系统的分散控制与鲁棒控制[M].西安:西北工业大学出版社,1997.
[20]沃松林,史国栋,邹云.广义大系统的渐进稳定与镇定[J].电机与控制学报,2005,9(3):222-225.
[21]何汉林.数值分析[M].2版.北京:科学出版社,2011.