显式模型预测控制(explicit model predictive control,EMPC)避免了传统的模型预测控制中最为繁琐的反复在线优化过程.显式模型预测控制系统分为离线计算获得每个分区上控制律和在线查找控制律这两个不同阶段.离线计算阶段通过多参数二...显式模型预测控制(explicit model predictive control,EMPC)避免了传统的模型预测控制中最为繁琐的反复在线优化过程.显式模型预测控制系统分为离线计算获得每个分区上控制律和在线查找控制律这两个不同阶段.离线计算阶段通过多参数二次规划(multi-parametric quadratic program,mp-QP)对系统状态空间进行凸划分,并计算得到系统在每个状态分区上的分段仿射(piece-wise affine,PWA)控制律;在线计算阶段通过查表确定系统当前状态所在的分区(即进行点定位运算)从而直接得到相应的控制律.研究工作在于如何快速确定系统当前状态所在的分区,属于在线计算过程范畴.文章在离线计算所得的状态分区数据基础上,根据可达域的思想,设计可达分区点定位算法使在线计算时搜索范围大幅减少,从而显著降低在线计算所需时间,提高EMPC系统的实时性.通过两个仿真实验将可达分区算法与直接查找法相互对比,证明可达分区算法的优势.作为一个应用例子,将文章显式模型预测控制可达分区点定位算法用于直流无刷电机显式模型预测控制,表明所用方法的有效性.展开更多
For symbolic reachability analysis of rectangular hybrid systems, the basic issue is finding a formal structure to represent and manipulate its infinite state spaces. Firstly, this structure must be closed to the reac...For symbolic reachability analysis of rectangular hybrid systems, the basic issue is finding a formal structure to represent and manipulate its infinite state spaces. Firstly, this structure must be closed to the reachability operation which means that reachable states from states expressed by this structure can be presented by it too. Secondly, the operation of finding reachable states with this structure should take as less computation as possible. To this end, a constraint system called rectangular zone is formalized, which is a conjunction of fixed amount of inequalities that compare fixed types of linear expressions with two variables to rational numbers. It is proved that the rectangular zone is closed to those reachability operations-intersection, elapsing of time and edge transition. Since the number of inequalities and the linear expression of each inequality is fixed in rectangular zones, so to obtain reachable rectangular zones, it just needs to change the rational numbers to which these linear expressions need to compare. To represent rectangular zones and unions of rectangular zones, a data structure called three dimensional constraint matrix(TDCM) and a BDD-like structure rectangular hybrid diagram(RHD) are introduced.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.61373043&61003079)the Fundamental Research Funds for the Central Universities(Grant No.JB140316)
文摘For symbolic reachability analysis of rectangular hybrid systems, the basic issue is finding a formal structure to represent and manipulate its infinite state spaces. Firstly, this structure must be closed to the reachability operation which means that reachable states from states expressed by this structure can be presented by it too. Secondly, the operation of finding reachable states with this structure should take as less computation as possible. To this end, a constraint system called rectangular zone is formalized, which is a conjunction of fixed amount of inequalities that compare fixed types of linear expressions with two variables to rational numbers. It is proved that the rectangular zone is closed to those reachability operations-intersection, elapsing of time and edge transition. Since the number of inequalities and the linear expression of each inequality is fixed in rectangular zones, so to obtain reachable rectangular zones, it just needs to change the rational numbers to which these linear expressions need to compare. To represent rectangular zones and unions of rectangular zones, a data structure called three dimensional constraint matrix(TDCM) and a BDD-like structure rectangular hybrid diagram(RHD) are introduced.
