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Extraction of a computer-certified ODE solver
arXiv - CS - Logic in Computer Science Pub Date : 2021-04-06 , DOI: arxiv-2104.02536
Grigory Devadze, Lars Flessing, Stefan Streif

Reliably determining system trajectories is essential in many analysis and control design approaches. To this end, an initial value problem has to be usually solved via numerical algorithms which rely on a certain software realization. Because software realizations can be error-prone, proof assistants may be used to verify the underlying mathematical concepts and corresponding algorithms. In this work we present a computer-certified formalization of the solution of the initial value problem of ordinary differential equations. The concepts are performed in the framework of constructive analysis and the proofs are written in the \texttt{Minlog} proof system. We show the extraction of a program, which solves an ODE numerically and provide some possible optimization regarding the efficiency. Finally, we provide numerical experiments to demonstrate how programs of a certain high level of abstraction can be obtained efficiently. The presented concepts may also be viewed as a part of preliminary work for the development of formalized nonlinear control theory, hence offering the possibility of computer-assisted controller design and program extraction for the controller implementation.

中文翻译:

提取计算机认证的ODE求解器

在许多分析和控制设计方法中,可靠地确定系统轨迹至关重要。为此,通常必须通过依赖特定软件实现的数值算法来解决初始值问题。由于软件实现可能容易出错,因此可以使用证明助手来验证基础的数学概念和相应的算法。在这项工作中,我们提出了计算机认证的常微分方程初值问题解的形式化方法。这些概念是在构造分析的框架中执行的,并且证明是在\ texttt {Minlog}证明系统中编写的。我们展示了一个程序的提取,该提取可以用数值方式求解ODE并提供一些关于效率的可能的优化。最后,我们提供了数值实验,以演示如何可以高效地获得某些高抽象水平的程序。提出的概念也可以看作是形式化非线性控制理论发展的前期工作的一部分,因此提供了计算机辅助控制器设计和控制器实现程序提取的可能性。
更新日期:2021-04-08
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