This paper presents an iterative algorithm to compute a Robust Control Invariant (RCI) set, along with an invariance-inducing control law, for Linear Parameter-Varying (LPV) systems. As the real-time measurements of the scheduling parameters are typically available, in the presented formulation, we allow the RCI set description along with the invariance-inducing controller to be scheduling parameter dependent. The considered formulation thus leads to parameter-dependent conditions for the set invariance, which are replaced by sufficient Linear Matrix Inequality (LMI) conditions via Polya's relaxation. These LMI conditions are then combined with a novel volume maximization approach in a Semidefinite Programming (SDP) problem, which aims at computing the desirably large RCI set. In addition to ensuring invariance, it is also possible to guarantee performance within the RCI set by imposing a chosen quadratic performance level as an additional constraint in the SDP problem. The reported numerical example shows that the presented iterative algorithm can generate invariant sets which are larger than the maximal RCI sets computed without exploiting scheduling parameter information.

中文翻译：

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具有保证性能的 LPV 模型的参数相关鲁棒不变量集的计算

本文提出了一种迭代算法，用于计算线性参数变化 (LPV) 系统的鲁棒控制不变量 (RCI) 集以及引入不变性的控制律。由于调度参数的实时测量通常是可用的，在所提出的公式中，我们允许 RCI 集描述以及不变性诱导控制器依赖于调度参数。因此，所考虑的公式导致集合不变性的参数相关条件，这些条件通过 Polya 松弛被足够的线性矩阵不等式 (LMI) 条件所取代。然后将这些 LMI 条件与半定规划 (SDP) 问题中的新颖体积最大化方法相结合，该方法旨在计算所需的大 RCI 集。除了保证不变性，还可以通过将选定的二次性能级别作为 SDP 问题中的附加约束来保证 RCI 集内的性能。报告的数值示例表明，所提出的迭代算法可以生成大于计算的最大 RCI 集而不利用调度参数信息的不变集。