多胞约束LPV系统多面体不变集RMPC算法
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摘要
针对一类输入和输出受约束且具有多胞结构的离散LPV系统,提出一种基于多面体不变集的鲁棒模型预测控制(RMPC)算法.选取一系列收敛于原点的离散状态点,计算每个状态的反馈控制率,构建相应的多面体不变集.在每一个采样时刻,确定包含当前状态的最小多面体不变集,通过计算与相邻两个多面体不变集的位置关系,执行连续的状态反馈控制率.仿真结果表明,相比椭圆不变集离线RMPC算法,所提出算法扩大了系统的稳定区域,取得了保守性较小的结果.
Based on the polyhedral invariant sets,a robust model predictive control algorithm is developed for an inputconstrained and output-constrained polytopic linear parameter varying discrete system.A sequence of discrete states converging to the origin is chosen to compute the corresponding state feedback control laws,and also construct each polyhedral invariant sets.At each sampling time,the smallest polyhedral invariant sets that the current measured state can be embedded is determined.The continuous state feedback control laws based on the position of the current measured state between the adjacent polyhedral invariant sets are implemented.Simulation results show that,compared to the ellipsoidal off-line RMPC algorithm,the proposed algorithm yields a substantial expansion of the region stabilized and achieves a less conservative result.
Based on the polyhedral invariant sets,a robust model predictive control algorithm is developed for an inputconstrained and output-constrained polytopic linear parameter varying discrete system.A sequence of discrete states converging to the origin is chosen to compute the corresponding state feedback control laws,and also construct each polyhedral invariant sets.At each sampling time,the smallest polyhedral invariant sets that the current measured state can be embedded is determined.The continuous state feedback control laws based on the position of the current measured state between the adjacent polyhedral invariant sets are implemented.Simulation results show that,compared to the ellipsoidal off-line RMPC algorithm,the proposed algorithm yields a substantial expansion of the region stabilized and achieves a less conservative result.
引文
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[15]Bumroongsri P,Kheawhom S.An off-line robust MPC algorithm for uncertain polytopic discrete-time systems using polyhedral invariant sets[J].J of Process Control,2012,22(5):975-983.
[16]席裕庚,朱红林,李德伟.基于多面体不变集的离线鲁棒预测控制器综合[J].控制与决策,2009,24(2):187-191.(Xi Y G,Zhu H L,Li D W.Synthesizing off-line robust model predictive control based on polyhedron invariant set[J].Control and Decision,2009,24(2):187-191.)
[17]高宪文,张立,王介生,等.变约束高效预测控制[J].控制理论与应用,2011,28(6):855-860.(Gao X W,Zhang L,Wang J S,et al.Efficient modelpredictive control with variable constraints[J].Control Theory&Applications,2011,28(6):855-860.)
[2]Petres Z.Polytopic decomposition of linear parameter-varying models by tensor-product model transformation[D].Budapest:Budapest University of Technology and Economics,2006.
[3]Kanev S,Verhaegen M.Robust asymptotically stable finitehorizon MPC[J].Automatica,2006,42(12):2189-2194.
[4]席裕庚.预测控制[M].北京:国防科技出版社,1993:1-10.(Xi Y G.Model predictive control[M].Beijing:National Defense Publishing House,1993:1-10.)
[5]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.(Xi Y G,Li D W.Fundamental philosophy and status of qualitative synthesis of model predictive control[J].Acta Automatica Sinica,2008,34(10):1225-1234.)
[6]Wan Z Y,Kothare M V.An efficient off-line formulation of robust model predictive control using linear matrix ineqalitese[J].Automatica,2003,39(5):837-846.
[7]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.(Ding B C,Yang P.Synthesizing off-line robust model predictive controller based on nominal performance cost[J].Acta Automatica Sinica,2006,32(2):304-310.)
[8]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.(Ding B C,Zou T.Synthesizing output feedback predictive control for constrained uncertain time-varying discrete systems[J].Acta Automatica Sinica,2007,33(1):78-83.)
[9]Wan Z Y,Kothare M V.Robust output feedback model predictive control using off-line linear matrix inequalities[J].J of Process Control,2002,12(2):763-774.
[10]李小军,丁宝苍,牛永肖.基于部分闭环优化的约束鲁棒调节器的新方法[C].2006中国控制与决策学术年会.天津,2006:133-136.(Li X J,Ding B C,Niu Y X.A synthesis approach of constrained robust regulation based on partial closedloop optimization[C].Proc of 2006 Chinese Control and Decision Conf.Tianjin,2006:133-136.)
[11]牛永肖,丁宝苍,孙鹤旭.输入非线性系统的两步法预测控制的鲁棒稳定性[J].控制与决策,2006,21(4):457-461.(Niu Y X,Ding B C,Sun H X.Robust stability of two-step predictive control for systems with input nonlinearities[J].Control and Decision,2006,21(4):457-461.)
[12]Gilbert E G,Tan K T.Linear systems with state and control constraints:The theory and application of maximal output admissible sets[J].IEEE Trans on Automatic Control,1991,36(9):1008-1020.
[13]Kothare M V,Balakrishnan V.Robust constrained model predictive control using linear matrix inequalities[J].Automatica,1996,32(10):1361-1379.
[14]Pluymers B,Rossiter J A,Suykens J A K,et al.The efficient computation of polyhedral invariant sets for linear systems with polytopic uncertainty[C].Proc of the American Control Conf.Portland,2005:1296-1304.
[15]Bumroongsri P,Kheawhom S.An off-line robust MPC algorithm for uncertain polytopic discrete-time systems using polyhedral invariant sets[J].J of Process Control,2012,22(5):975-983.
[16]席裕庚,朱红林,李德伟.基于多面体不变集的离线鲁棒预测控制器综合[J].控制与决策,2009,24(2):187-191.(Xi Y G,Zhu H L,Li D W.Synthesizing off-line robust model predictive control based on polyhedron invariant set[J].Control and Decision,2009,24(2):187-191.)
[17]高宪文,张立,王介生,等.变约束高效预测控制[J].控制理论与应用,2011,28(6):855-860.(Gao X W,Zhang L,Wang J S,et al.Efficient modelpredictive control with variable constraints[J].Control Theory&Applications,2011,28(6):855-860.)