CAREER: Algorithms and Fundamental Limitations for Sparse Control

该建议是研究反馈控制策略的设计，稳定和转向系统的影响，他们只有几个变量。其动机来自大规模或地理分布的应用程序，因此在许多地方无法切实受到影响。一个主要的激励应用是控制人体内的代谢化学反应网络，该网络可能受到药物的影响，这些药物通常只与人体代谢中数万种试剂中的几种相互作用。我们的目标是设计稀疏的战略，稳定模型的代谢网络远离不良的平衡，着眼于发展的算法，有一天可以用来设计药物调节人体metabolis.Intellectual优点：有效的算法，找到sparteries可能的控制器的线性和多项式动力系统的设计将进行研究。每当这是不可能的棘手的结果，严格证明这是不可能的，将开发。工作的一个中心焦点将是计算复杂性问题，因为在许多感兴趣的情况下，稀疏控制器的搜索是难以处理的。主要的贡献将是在算法的发展，利用现实世界中的系统的通用属性，以避免棘手的障碍，并有效地找到非常稀疏的controllers.Broader影响：该算法有可能成为控制工程实践的标准工具，每当涉及到大型系统或传感器和执行器的数量是有限的。PI将努力确保此处开发的协议进入控制课程。本科生和研究生都将参与研究的执行。计划开展外联活动，特别是针对刚开始的本科生，目的是提高工程学中代表性不足群体的保留率。

The proposal is to study the design of feedback control strategies which stabilize and steer systems by affecting them in only a few variables. The motivation comes from applications which are either large-scale or geographically distributed and therefore cannot be feasibly affected in many places. A primary motivating application is the control of metabolic chemical reaction networks within the human body which can be affected by drugs typically interacting with only a few out of the tens of thousands reagents in the human metabolism. The goal is to design sparse strategies which stabilize models of metabolic networks away from undesirable equilibria with an eye to developing algorithms which could one day be used to design drugs regulating human metabolism.Intellectual Merit:The design of efficient algorithms which find the sparsest possible controllers for linear and polynomial dynamical systems will be investigated. Whenever this is not possible intractability results rigorously demonstrating this impossibility will be developed. A central focus of the work will be on computational complexity issues as the search for sparse controllers turns out to be intractable in many cases of interest. The main contribution will be in the development of algorithms which take advantage of the generic properties of real-world systems to avoid intractability barriers and efficiently find very sparse controllers.Broader Impacts:The algorithms have potential to become standard tools of control engineering practice whenever large systems are involved or when the number of sensors and actuators available is limited. The PI will work to ensure that the protocols developed here enter into the control curriculum. Both undergraduate and graduate students will be involved in the execution of the research. Outreach activities are planned, especially for beginning undergraduate students with the aim of increasing retention rates of under-represented groups in engineering.