We study the problem of constructing the control driving a controlled differential equation from discrete observations of the response. By restricting the control to the space of piecewise linear paths, we identify the assumptions that ensure uniqueness. The main contribution of this paper is the introduction of a novel numerical algorithm for the construction of the piecewise linear control, that converges uniformly in time. Uniform convergence is needed for many applications and it is achieved by approaching the problem through the signature representation of the paths, which allows us to work with the whole path simultaneously.

翻译：我们从对反应的离散观测中研究构建控制驱动控制差异方程式的问题。通过将控制限制在片断线性路径的空间,我们确定了确保独特性的各种假设。本文的主要贡献是采用新的数字算法来构建片断线性控管,这种算法在时间上趋同。许多应用需要统一趋同,通过路径的签名表示来解决这一问题,从而使我们能够同时与整个路径合作。