CAREER: Algorithms and Fundamental Limitations for Sparse Control

我们的建议是研究反馈控制策略的设计，通过只在几个变量中影响系统来稳定和操纵系统。动机来自大规模或地理分布的应用程序，因此在许多地方不可能受到可行的影响。一个主要的激励应用是控制人体内的代谢化学反应网络，该网络可能会受到药物的影响，通常只与人体新陈代谢的数万种试剂中的几种相互作用。目标是设计稀疏策略，使代谢网络模型远离不良平衡，着眼于开发有朝一日可用于设计调节人类新陈代谢的药物的算法。智力优势：将研究为线性和多项式动态系统找到最稀疏可能控制器的高效算法的设计。只要这是不可能的，就会产生严格证明这一不可能性的棘手结果。这项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，稀疏控制器的搜索被证明是难以解决的。主要的贡献将是开发算法，该算法利用真实世界系统的一般特性来避免难以处理的障碍，并有效地找到非常稀疏的控制器。广泛的影响：每当涉及大型系统或可用的传感器和执行器数量有限时，这些算法都有可能成为控制工程实践的标准工具。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这项研究的实施。计划开展外联活动，特别是针对初学本科生，目的是提高工程学专业任职人数不足群体的留存率。

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.