In addition to perfectly steering the output concentration of a process network to an exogenous set-point, a desired synthetically implemented biological controller should be able to robustly maintain this regulated output in the face of the extrinsic disturbances and inherent uncertainties due to an ever-varying environment besides the imprecise modeling. Such an ability, which is called robust perfect adaptation (RPA), can be achieved by integral feedback control (IFC). Answering how IFC is (biochemically) constructible in generally unknown synthetic networks has been a research focus in the community. One of these answers, which has been well investigated previously, is to utilize a simple (Hill-type) integral negative feedback controller. Another effective solution, which has made significant progress, is the increasingly being used antithetic integral feedback controller. In this article, by applying these two RPA-achieving controllers in control of an uncertain process network with an arbitrary number of species, the behavior of the resulting closed-loop systems, in which the effect of molecular dilution is also considered, is analyzed. Through this analysis, by assuming that the stability is preserved, it is shown that the latter controller can be approximately reduced to the former (simpler) one by individually increasing one of its parameters (the annihilation rate). Furthermore, to address the stability assumption, exact parametric conditions are derived to guarantee the stability of the control systems. These findings can lead us to gain a deeper insight into and to simplify the robust design, performance analysis, and implementation of such living circuits. Simulation results accompany this article's analytical elaborations.

中文翻译：

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合成生物学启发的鲁棒完美适应控制系统：模型简化和稳定性分析

除了将过程网络的输出浓度完美地控制在外源设定点之外，所需的合成实现的生物控制器还应能够面对外部变化和不断变化带来的内在不确定性，稳健地维持这一调节后的输出除了不精确的建模之外的环境。可以通过积分反馈控制（IFC）实现这种功能，称为鲁棒完美自适应（RPA）。解答国际金融公司如何（生物化学地）在通常未知的合成网络中进行构建一直是社区研究的重点。这些答案之一（已在前面进行了深入研究）是利用简单的（希尔式）积分负反馈控制器。另一项有效的解决方案已取得重大进展，是越来越多地使用的对数积分反馈控制器。在本文中，通过将这两个实现RPA的控制器应用于具有任意种类的不确定过程网络的控制，分析了所得的闭环系统的行为，其中还考虑了分子稀释的影响。通过该分析，通过假设保持稳定性，可以表明，通过单独增加其参数之一（an灭率），可以将后一种控制器近似减少到前一种（简单）控制器。此外，为了解决稳定性假设，需要导出精确的参数条件以保证控制系统的稳定性。这些发现可以使我们深入了解并简化健壮的设计，性能分析，并实现这种活动电路。仿真结果与本文的分析阐述一起进行。