CAREER: Algorithms and Fundamental Limitations for Sparse Control

本课题的目的是研究一种反馈控制策略的设计，这种控制策略通过对系统进行少量的影响来实现系统的稳定和转向。动机来自于大规模或地理分布的应用程序，因此不可能在许多地方受到影响。一个主要的激励应用是控制人体内的代谢化学反应网络，这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。目标是设计稀疏策略，稳定代谢网络模型，使其远离不希望的平衡，并着眼于开发有朝一日可用于设计调节人体代谢的药物的算法。智力优势：设计有效的算法，为线性和多项式动力系统寻找尽可能稀疏的控制器将被研究。每当这是不可能的，棘手的结果严格证明这种不可能将发展。工作的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，搜索稀疏控制器变得难以处理。主要的贡献将是在算法的发展，利用现实世界系统的一般性质，以避免棘手的障碍，并有效地找到非常稀疏的控制器。更广泛的影响：当涉及大型系统或可用的传感器和执行器数量有限时，这些算法有可能成为控制工程实践的标准工具。PI将努力确保这里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。计划开展外展活动，特别是针对本科新生，目的是提高工程专业代表性不足群体的留校率。

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.