Time delays are ubiquitous in industry, and they must be accounted for when designing control strategies. However, numerical optimal control (NOC) of delay differential equations (DDEs) is challenging because it requires specialized discretization methods and the time delays may depend on the manipulated inputs or state variables. Therefore, in this work, we propose to linearize the delayed states around the current time. This results in a set of implicit differential equations, and we compare the steady states and the corresponding stability criteria of the DDEs and the approximate system. Furthermore, we propose a simultaneous approach for NOC of DDEs based on the linearization, and we discretize the approximate system using Euler's implicit method. Finally, we present a numerical example involving a molten salt nuclear fission reactor.

翻译：时滞在工业中普遍存在，在设计控制策略时必须予以考虑。然而，时滞微分方程（DDEs）的数值最优控制（NOC）具有挑战性，因为它需要专门的离散化方法，并且时滞可能依赖于操纵输入或状态变量。因此，在本工作中，我们提出在当前时间附近对时滞状态进行线性化。这产生了一组隐式微分方程，我们比较了DDEs与近似系统的稳态及其相应的稳定性判据。此外，我们提出了一种基于该线性化的、用于DDEs数值最优控制的同步方法，并使用欧拉隐式方法对近似系统进行离散化。最后，我们给出了一个涉及熔盐核裂变反应堆的数值算例。