A Singular Singular Perturbation Problem Arising From a Class of Biomolecular Feedback Controllers
A Singular Singular Perturbation Problem Arising From a Class of Biomolecular Feedback Controllers
复制标题
一类生物分子反馈控制器引起的奇异奇异扰动问题
DOI：
10.1109/lcsys.2018.2845547
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发表时间：
2019
影响因子：
3
通讯作者：
Domitilla Del Vecchio
中科院分区：
文献类型：
--
作者：
Y. Qian;Domitilla Del Vecchio
合成生物学的一个长期挑战是设计出能够在高度不确定的细胞环境中稳定运行的生物分子系统。最近，人们对设计生物分子反馈控制器来解决这一挑战越来越感兴趣。分子封存是一种被提出的反馈机制。对于这种类型的设计，当控制器内的所有反应都足够快时，无论参数不确定性如何，过程输出都可以达到设定点。然而，正如我们在这封信中所证明的那样，分子封存影响快速控制器动力学的方式导致了一个奇异奇异摄动（SSP）系统。在SSP系统中，边界层雅可比矩阵是奇异的，因此不能应用标准的奇异摄动方法，这给分析确定基于隔离的控制器的性能带来了困难。在这封信中，我们考虑一类线性系统，它捕获了基于隔离的控制器的关键结构。我们证明，在一定的技术条件下，这些SSP系统仍然可以被依赖于小参数的降阶系统所近似。这一结果使我们能够分析地评估基于隔离的控制器的线性化模型的跟踪性能。
A long-standing challenge in synthetic biology is to engineer biomolecular systems that can perform robustly in highly uncertain cellular environments. Recently, there has been increasing interest to design biomolecular feedback controllers to address this challenge. Molecular sequestration is one of the proposed feedback mechanisms. For this type of design, when all reactions within the controller are sufficiently fast, the process output can reach a set-point regardless of parametric uncertainties. However, as we demonstrate in this letter, the way in which molecular sequestration affects the fast controller dynamics leads to a singular singularly perturbed (SSP) system. In an SSP system, the boundary layer Jacobian is singular and thus standard singular perturbation approaches cannot be applied, posing difficulties to analytically determine the performance of sequestration-based controllers. In this letter, we consider a class of linear systems that capture the key structure of sequestration-based controllers. We show that, under certain technical conditions, these SSP systems can still be approximated by reduced-order systems that are dependent on the small parameter. This result allows us to analytically evaluate the tracking performance of the linearized model of a sequestration-based controller.