网络化系统对非预期相互作用的鲁棒性及其在工程遗传电路中的应用
Robustness of networked systems to unintended interactions with application to engineered genetic circuits
摘要：
一个网络化的动力系统是由多个子系统通过预定的相互作用相互连接而成的。然而，在许多工程应用中，一个子系统也可以通过“非预期”的交互影响其他子系统，这可能会严重阻碍预期网络的行为。虽然非预期的相互作用可以建模为干扰输入的子系统，这些干扰依赖于网络的状态。因此，每个隔离子系统的干扰衰减特性单独地不足以确保网络行为对于非预期的交互是鲁棒的。在本文中，我们提供了充分的条件，子系统的动力学和相互作用的地图，使网络的行为是鲁棒的非预期的相互作用。这些条件要求每个子系统衰减恒定的外部干扰，是单调或“近单调”，非预期的相互作用地图是单调的，和规定的相互作用地图不包含反馈回路。我们利用这一结果来指导资源有限的遗传电路的设计。更一般地说，我们的研究结果提供了条件下，组成子系统的鲁棒性足以保证网络的鲁棒性，以意外的相互作用。
英文摘要：
A networked dynamical system is composed of subsystems interconnected through prescribed interactions. In many engineering applications, however, one subsystem can also affect others through "unintended" interactions that can significantly hamper the intended network's behavior. Although unintended interactions can be modeled as disturbance inputs to the subsystems, these disturbances depend on the network's states. As a consequence, a disturbance attenuation property of each isolated subsystem is, alone, insufficient to ensure that the network behavior is robust to unintended interactions. In this paper, we provide sufficient conditions on subsystem dynamics and interaction maps, such that the network's behavior is robust to unintended interactions. These conditions require that each subsystem attenuates constant external disturbances, is monotone or "near-monotone", the unintended interaction map is monotone, and the prescribed interaction map does not contain feedback loops. We employ this result to guide the design of resource-limited genetic circuits. More generally, our result provide conditions under which robustness of constituent subsystems is sufficient to guarantee robustness of the network to unintended interactions.
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