Combinatorial Approach Toward Multiparametric Quadratic Programming Based on Characterizing Adjacent Critical Regions
Combinatorial Approach Toward Multiparametric Quadratic Programming Based on Characterizing Adjacent Critical Regions
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DOI：
10.1109/tac.2018.2791479
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发表时间：
2018-01
影响因子：
6.8
通讯作者：
Parisa Ahmadi-Moshkenani;T. Johansen;Sorin Olaru
中科院分区：
文献类型：
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作者：
Parisa Ahmadi-Moshkenani;T. Johansen;Sorin Olaru
一些基于优化的控制设计技术可以以参数优化问题的形式出现。多参数二次规划（mpQP）代表了一个流行的类往往与约束线性系统的控制。完整的解决方案mpQP采取显式反馈函数的形式与分段仿射结构，有效的多面体分区的可行参数空间被称为临界区域。最近提出的组合方法求解mpQP已显示出更好的效率比几何方法在寻找完整的解决方案的问题与高维的参数向量。另一方面，这种方法的缺点是，随着问题中约束数量的增加，它往往变得非常慢。本文提出了一种基于相邻临界区域及其对应的最优活动集的理论性质来枚举mpQP中所有最优活动集的替代方法。因此，它导致从调查中排除大量可行但不是最佳的候选活动集。因此，应该解决的线性规划的数量明显减少，算法变得更快。仿真结果证实了所提出的方法的可靠性，在找到完整的解决方案的mpQP，同时减少计算时间相比，有利的最佳替代方法。
Several optimization-based control design techniques can be cast in the form of parametric optimization problems. The multiparametric quadratic programming (mpQP) represents a popular class often related to the control of constrained linear systems. The complete solution to mpQP takes the form of explicit feedback functions with a piecewise affine structure, valid in polyhedral partitions of the feasible parameter space known as critical regions. The recently proposed combinatorial approach for solving mpQP has shown better efficiency than geometric approaches in finding the complete solution to problems with high dimensions of the parameter vectors. The drawback of this method, on the other hand, is that it tends to become very slow as the number of constraints increases in the problem. This paper presents an alternative method for enumerating all optimal active sets in an mpQP based on theoretical properties of adjacent critical regions and their corresponding optimal active sets. Consequently, it results in excluding a noticeable number of feasible but not optimal candidate active sets from investigation. Therefore, the number of linear programs that should be solved decreases noticeably and the algorithm becomes faster. Simulation results confirm the reliability of the suggested method in finding the complete solution to the mpQPs while decreasing the computational time compared favorably with the best alternative approaches.