带有界干扰的LPV系统鲁棒预测控制综合方法
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摘要
针对带有界干扰的多胞描述约束LPV系统,提出一种鲁棒预测控制综合方法,设计保证系统闭环稳定的状态反馈控制器。为减少计算的复杂性,采用线性矩阵不等式求解预测控制无穷时域最小-最大优化问题,获得状态反馈控制律,将该控制率施加到系统,证明了算法的可行性和系统的闭环稳定性。通过仿真实验验证了算法有效性。
Consider a kind of polytopic described LPV system with bounded disturbances,a synthesis of robust model predictive control is proposed,which adopts a category of state feedback controller. In order to reduce the computational complexity,a stability guaranteed state feedback control law is achieved by solving the min-max optimization problem of the worst-case infinite time horizon cost function. And the proposed robust MPC algorithm can asymptotically stabilized the state-delayed LPV system. And an example proves the effectiveness of the algorithm.
Consider a kind of polytopic described LPV system with bounded disturbances,a synthesis of robust model predictive control is proposed,which adopts a category of state feedback controller. In order to reduce the computational complexity,a stability guaranteed state feedback control law is achieved by solving the min-max optimization problem of the worst-case infinite time horizon cost function. And the proposed robust MPC algorithm can asymptotically stabilized the state-delayed LPV system. And an example proves the effectiveness of the algorithm.
引文
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[15]Ding B,Xi Yu,Cychowski M T,et al.An synthesis approach for out put feedback robust constrained model predictive control[J].Automatic,2008,44(1):258-264.
[2]席裕庚.预测控制[M].北京:国防科技出版社,2003.
[3]席裕庚,李德伟.预测控制定性综合理论的基本思路和研究现状[J].自动化学报,2008,34(10):1225-1234.
[4]丁宝仓,杨鹏.基于标称性能指标的离线鲁棒预测控制综合[J].自动化学报,2006,32(2):304-310.
[5]丁宝仓,邹涛.约束时变不确定系统的输出反馈预测控制综合[J].自动化学报,2007,33(1):78-83.
[6]Kothare M,Balakrishnan V,Morari M.Robust constrained model predictive control using linear matrix inequalities[J].Automatica,1996,32(10):1361-1379.
[7]Kanev S,Verhaegen M.Roust asymptotically stablefinitehorizon MPC[J].Automatic,2006,42(12):2189-2194.
[8]王明昊,刘刚,赵鹏涛,等.多胞约束LPV系统多面体不变集RMPC算法[J].控制与决策,2013,28(11):1661-1666.
[9]赵敏.基于离线状态观测器的LPV系统预测控制[J].控制工程,2013,20(6):1671-7848.
[10]黄骅,何德峰,俞立.基于多面体描述系统的鲁棒非线性预测控制[J].自动化学报,2012,38(12):1906-1912.
[11]Limon D,Alamo T,Salas F,et al.Input to state stability of min-max MPC controllers for nonlinear systems with bounded uncertainties[J].Automatica,2006,42(5):797-803.
[12]Ding B.Constrained robust model predictive control via parameter dependent dynamic output feedback[J].Automatica,2010,46(9):1517-1523.
[13]Boyd S L,Ghaoui E F,Feron E,et al.Linear matrix inequalities in system and control theory[C].Philadelphia,PA:Studies in Applied Mathematics,1994.
[14]丁宝苍.预测控制的理论与方法[M].北京:机械工业出版社,2008.
[15]Ding B,Xi Yu,Cychowski M T,et al.An synthesis approach for out put feedback robust constrained model predictive control[J].Automatic,2008,44(1):258-264.