离线椭圆集的非线性模型预测控制算法研究
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摘要
针对一类带有约束的非线性系统,提出一种非线性时间最优模型预测控制算法。这种方法首先基于Jacobian线性化将非线性进行线性化,能够推导一系列凸优化问题,而且产生的线性化误差在Lipschitz条件下确定上边界范围。然后采用双重模式策略,在离线情况下构造一系列椭圆集来描述t步可行区域,每个椭圆集的平衡点根据上一个椭圆来选取,最后再根据在线计算合适的输入使系统稳定。采用逐步倒退计算的方法能够确保迭代的可行性和稳定性,大大减少了计算负担。数值例子证明了算法的有效性。
A new nonlinear time optimal model predictive control paradigm is proposed for a class of nonlinear system with constraints. Firstly, this method of nonlinear linearized based on Jacobian linearization is used to be derive a series of convex optimization problem, and the linearization error determines the upper boundary under Lipschitz conditions. Then it uses dual model strategy, in the case of offline condition step structures a series of ellipsoid sets to describe t step feasible region, balance point of each ellipsoid sets is based on an ellipsoid to choose, according to the ellipsoid sets suitable input,it makes the system stable by online computation. Using a step by step backwards computation method can ensure the feasibility and stability of the iteration, and reduce the computation burden greatly. Numerical examples prove the feasibility of the algorithm.
A new nonlinear time optimal model predictive control paradigm is proposed for a class of nonlinear system with constraints. Firstly, this method of nonlinear linearized based on Jacobian linearization is used to be derive a series of convex optimization problem, and the linearization error determines the upper boundary under Lipschitz conditions. Then it uses dual model strategy, in the case of offline condition step structures a series of ellipsoid sets to describe t step feasible region, balance point of each ellipsoid sets is based on an ellipsoid to choose, according to the ellipsoid sets suitable input,it makes the system stable by online computation. Using a step by step backwards computation method can ensure the feasibility and stability of the iteration, and reduce the computation burden greatly. Numerical examples prove the feasibility of the algorithm.
引文
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[15]Lee Y I,Kouvaritakis B,Cannon M.Constrained receding horizon predictive control for nonlinear systems[J].Automatica,2002,38(12):2093-2102.
[16]Mees A I.Achieving diagonal dominance[J].Systems&Control Letters,1981,1(3):155-158.
[17]Wan Z,Kothare M V.An efficient off-line formulation of robust model predictive control using linear matrix inequalities[J].Automatica,2003,39(5):837-846.
[18]Cannon M,Ng D,Kouvaritakis B.Successive linearization NMPC for a class of stochastic nonlinear systems[M]//Nonlinear Model Predictive Control.Berlin Heidelberg:Springer,2009:249-262.
[2]Qifeng C,Aoyun M,Zhou W,et al.Time optimal MPC based on offline construction of ellipsoidal sets[C]//Proceedings of Chinese Control Conference,Hangzhou,China,2015:4145-4150.
[3]Lee Y I,Kouvaritakis B.Robust receding horizon predictive control for systems with uncertain dynamics and input saturation[J].Automatica,2000,36(10):1497-1504.
[4]Mayne D Q,Rawlings J B,Rao C V,et al.Constrained model predictive control:Stability and optimality[J].Automatica,2000,36(6):789-814.
[5]Rawlings J B,Mayne D Q.Model predictive control:Theory and design[M].[S.l.]:Nob Hill Publishing,LLC,2009:3430-3433.
[6]席裕庚,李德伟,林姝.模型预测控制——现状与挑战[J].自动化学报,2013,39(3):222-236.
[7]习春苗.电力工业模型预测控制——现状与发展[J].环球市场信息导报,2016(9):133.
[8]何德峰,丁宝苍,于树友.非线性系统模型预测控制若干基本特点与主题回顾[J].控制理论与应用,2013,30(3):273-287.
[9]Broeck L V D,Diehl M,Swevers J.A model predictive control approach for time optimal point-to-point motion control[J].Mechatronics,2011,21(7):1203-1212.
[10]Janssens P,van Loock W,Pipeleers G,et al.An efficient algorithm for solving time-optimal point-to-point motion control problems[C]//Proceedings of IEEE International Conference on Mechatronics,2013:682-687.
[11]Wan Z,Kothare M V.An efficient off-line formulation of robust model predictive control using linear matrix inequalities[J].Automatica,2003,39(5):837-846.
[12]Rakovi S V,Kerrigan E C,Kouramas K I,et al.Invariant approximations of the minimal robust positively invariantset[J].IEEE Transactions on Automatic Control,2005,50(3):406-410.
[13]Kothare M V,Balakrishnan V,Morari M.Robust constrained model predictive control using linear matrix inequalities[C]//Proceedings of IEEE American Control Conference,1994:1361-1379.
[14]Cannon M,Buerger J,Kouvaritakis B,et al.Robust tubes in nonlinear model predictive control[J].IEEE Transactions on Automatic Control,2011,56(8):1942-1947.
[15]Lee Y I,Kouvaritakis B,Cannon M.Constrained receding horizon predictive control for nonlinear systems[J].Automatica,2002,38(12):2093-2102.
[16]Mees A I.Achieving diagonal dominance[J].Systems&Control Letters,1981,1(3):155-158.
[17]Wan Z,Kothare M V.An efficient off-line formulation of robust model predictive control using linear matrix inequalities[J].Automatica,2003,39(5):837-846.
[18]Cannon M,Ng D,Kouvaritakis B.Successive linearization NMPC for a class of stochastic nonlinear systems[M]//Nonlinear Model Predictive Control.Berlin Heidelberg:Springer,2009:249-262.