MISSILES：近似线性微分系统联合仿真耦合约束的全局线性化求解
MISSILES: an Efficient Resolution of the Co-simulation Coupling Constraint on Nearly Linear Differential Systems through a Global Linear Formulation
摘要：
在联合仿真环境中，微分方程的关联系统被单独求解，但它们在这些求解期间定期地彼此通信数据。为了提高稳定性和准确性，已经开发了迭代联合仿真方法。这样的方法意味着系统必须整合一个或多个时间每个协同仿真步骤（两个连续的通信之间的间隔），以找到最好的满足交换数据的接口值（根据给定的耦合约束）。这要求模块化模型中涉及的每个系统都能够回滚：能够重新整合已经与不同输入命令集成的时间间隔。在Eguillon等人于2022年介绍的一篇论文中，提出了COSTARICA过程，并将非回滚系统替换为迭代过程的非最后积分的估计器。本文介绍的MISSILES算法包括将COSTARICA过程应用于使用IFOSMONDI-JFM迭代联合仿真方法（由Eguillon等人于2021年引入）仿真的模块化模型的每个系统。实际上，在这种情况下，可以避免每个系统的估计器上的迭代部分，因为可以将协同仿真步骤上的全局分辨率写为单个全局线性系来求解。因此，MISSILES是一种非迭代法，与应用于使用COSTARICA过程模拟回滚的系统的IFOSMONDI-JFM迭代联合仿真方法相比，该方法可以得到相同的解。
英文摘要：
In a co-simulation context, interconnected systems of differential equations are solved separately but they regularly communicate data to one another during these resolutions. Iterative co-simulation methods have been developed in order to enhance both stability and accuracy. Such methods imply that the systems must integrate one or more times per co-simulation step (the interval between two consecutive communications) in order to find the best satisfying interface values for exchanged data (according to a given coupling constraint). This requires that every system involved in the modular model is capable of rollback: the ability to re-integrate a time interval that has already been integrated with different input commands. In a paper previously introduced by Eguillon et al. in 2022, the COSTARICA process is presented and consists in replacing the non-rollback-capable systems by an estimator on the non-last integrations of the iterative process. The MISSILES algorithm, introduced in this paper, consists in applying the COSTARICA process on every system of a modular model simulated with the IFOSMONDI-JFM iterative co-simulation method (introduced by Eguillon et al. in 2021). Indeed, in this case, the iterative part on the estimators of each system can be avoided as the global resolution on a co-simulation step can be written as a single global linear system to solve. Consequently, MISSILES is a non-iterative method that leads to the same solution than the IFOSMONDI-JFM iterative co-simulation method applied to systems using the COSTARICA process to emulate the rollback.
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