Optimizing a parameterized zonotope or ellipsoid is a common task in robust state estimation, fault diagnosis and reachability analysis. Recent studies have unified ellipsoids and zonotopes into basic ellipsotopes, which support precise representation for more nonlinear boundaries and constraints in practical applications. However, there are currently no available optimality criteria and optimization techniques for general basic ellipsotopes. In this paper, we introduce a novel optimality criterion called Schatten-p radius for basic ellipsotopes. Based on this criterion, we develop a set of methods to minimize the Schatten-p radius under convex constraints for arbitrary 0< p <∞, which also implies new available tools for minimizing zonotopes and ellipsoids. The effectiveness of the Schatten-p radius optimization is demonstrated on several numerical examples.

中文翻译：

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Schatten-p 半径：基本椭圆体的最优性准则和优化，适用于同位体和椭球体


优化参数化的 zonotope 或椭球体是稳健状态估计、故障诊断和可达性分析中的常见任务。最近的研究将椭球体和平行体统一为基本的椭圆体，这支持在实际应用中精确表示更多的非线性边界和约束。但是，目前没有适用于一般基本椭圆拓扑的最优性标准和优化技术。在本文中，我们介绍了一种新的最优性准则，称为基本椭圆体的 Schatten-p 半径。基于这个标准，我们开发了一套方法来在任意 0<p<∞ 的凸约束下最小化 Schatten-p 半径，这也意味着用于最小化同向体和椭球体的新可用工具。Schatten-p 半径优化的有效性在几个数值示例中得到了证明。