ABSTRACT A numerical method is proposed to reduce the complexity and computational effort involved in the application of the multiparametric linear programming technique in the design of offline controllers for linear systems subject to constraints. For this purpose, the concept of controlled invariant sets and the K q-flat data cluster analysis algorithm are applied. Specifically, we show how the K q-flat algorithm can be used to establish a smaller number of polyhedral regions associated with a piecewise affine explicit state feedback control law. We also propose a new approach in the design of sub-optimal controllers that further reduce the number of regions. Numerical examples show that a significant reduction in the complexity of the control law can be achieved by the proposed approach.

中文翻译：

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使用数据聚类分析为约束条件下的线性系统设计降低复杂度的控制器

摘要 提出了一种数值方法，以减少将多参数线性规划技术应用于受约束的线性系统的离线控制器设计中所涉及的复杂性和计算工作量。为此，应用了受控不变集的概念和 K q-flat 数据聚类分析算法。具体来说，我们展示了如何使用 K q-flat 算法来建立与分段仿射显式状态反馈控制律相关联的较少数量的多面体区域。我们还提出了一种设计次优控制器的新方法，进一步减少了区域的数量。数值例子表明，所提出的方法可以显着降低控制律的复杂性。