Advanced embedded algorithms are growing in complexity and they are an essential contributor to the growth of autonomy in many areas. However, the promise held by these algorithms cannot be kept without proper attention to the considerably stronger design constraints that arise when the applications of interest, such as aerospace systems, are safety-critical. Formal verification is the process of proving or disproving the ''correctness'' of an algorithm with respect to a certain mathematical description of it by means of a computer. This article discusses the formal verification of the Ellipsoid method, a convex optimization algorithm, and its code implementation as it applies to receding horizon control. Options for encoding code properties and their proofs are detailed. The applicability and limitations of those code properties and proofs are presented as well. Finally, floating-point errors are taken into account in a numerical analysis of the Ellipsoid algorithm. Modifications to the algorithm are presented which can be used to control its numerical stability.

中文翻译：

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用于模型预测控制的凸优化算法的验证和验证

先进的嵌入式算法越来越复杂，它们是许多领域自主性增长的重要贡献者。然而，如果不适当注意当感兴趣的应用（例如航空航天系统）对安全至关重要时出现的相当强的设计约束，就无法实现这些算法的承诺。形式验证是通过计算机证明或反驳算法相对于某种数学描述的“正确性”的过程。本文讨论了 Ellipsoid 方法的形式验证，一种凸优化算法，及其应用于后退水平控制的代码实现。详细介绍了编码代码属性及其证明的选项。还介绍了这些代码属性和证明的适用性和局限性。最后，在 Ellipsoid 算法的数值分析中考虑了浮点误差。提出了对算法的修改，可用于控制其数值稳定性。