Collaborative Research: Data Driven Control of Switched Systems with Applications to Human Behavioral Modification

急剧增加的医疗保健费用威胁着国家的经济。其中80%以上的费用是由慢性疾病造成的，这些疾病可以通过改变生活方式来预防或减轻。身体活动也是理想心血管健康的关键行为组成部分。这表明，通过个性化的虚拟健康顾问促进身体活动可以在广泛的人群中带来实质性的健康改善。受这些观察的启发，该提案旨在开发一个易于处理的实用框架，用于设计个性化的行为监测系统，旨在保持最佳的身体活动水平。这是通过将问题嵌入到一个更一般的系统理论中来实现的：具有可证明性能的控制器的设计，其特征在于系统由一系列模型组成，其中模型的数量和参数都不是先验已知的，并且必须从实验数据中获得，这些数据是从多个质量变化很大的传感器收集的。教育被积极地融入到这个项目中，从城市中学生的数据驱动建模STEM夏令营项目开始，并在大学阶段继续进行多学科项目，该项目使用个性化医学将从机器学习到系统理论和优化的各种不同学科联系起来。在研究生层面，这些活动得到了招聘工作的补充，这些招聘工作利用宾夕法尼亚州立大学麦克奈尔学者计划和东北大学多元文化工程计划的资源，以扩大代表性不足的群体对研究的参与。出于设计有效的行为干预的问题，该建议旨在开发一个全面的，计算上易于处理的框架，用于合成数据驱动的控制律的一类系统所描述的切换差分包含。这些模型出现在广泛的领域，从弹性基础设施到医疗保健，其特点是大量的不确定性和突然变化的动态。该研究解决了基于多项式优化及其与矩问题的连接的统一框架中的识别和控制设计问题。对识别领域的贡献包括开发一个易于处理的框架，用于不确定切换系统的鲁棒识别，该框架利用问题的基本结构来大幅降低计算复杂性，并且可以处理最坏情况和风险调整描述。对控制的贡献包括一个新的框架，机会约束控制的不确定切换系统，最大限度地实现所需的最终状态的概率，而在同一时间，最大限度地减少进入坏集的概率。作为一个证明的原则，由此产生的框架适用于设计基于智能手机的虚拟健康顾问能够提供个性化的最佳体力活动strategies.This奖反映了NSF的法定使命的问题，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

Dramatically increasing health care costs threaten the nation's economy. Over 80% of those costs are due to chronic illnesses which can be prevented or mitigated through lifestyle change. Physical activity is also a key behavioral component of ideal cardiovascular health. This suggests that promoting physical activity through the personalized virtual health advisors can lead to substantial health improvements across a broad spectrum of the population. Motivated by these observations, this proposal seeks to develop a tractable, practical framework for designing personalized behavior monitoring systems, aimed at maintaining optimal levels of physical activity. This is accomplished by embedding the problem into a more general, systems-theoretic one: design of controllers with provable performance for systems characterized by a collection of models where neither the number of models nor their parameters are a priori known and must be obtained from experimental data, collected from multiple sensors with large variations in quality. Education is proactively integrated into this project, starting with STEM summer camps projects for urban middle school students on data driven modeling and continuing at the college level with a multi-disciplinary program that uses personalized medicine to link a full range of distinct subjects ranging from machine learning to systems theory and optimization. At the graduate level, these activities are complemented by recruitment efforts that leverage the resources of Penn State's McNair Scholars Program and Northeastern University's Program in Multicultural Engineering to broaden the participation of underrepresented groups in research. Motivated by the problem of designing effective behavioral interventions, this proposal seeks to develop a comprehensive, computationally tractable framework for synthesizing data driven control laws for a class of systems described by switched difference inclusions. These models arise in a broad class of domains, ranging from resilient infrastructures to health care, characterized by large amounts of uncertainty and abruptly changing dynamics. The research addresses both the identification and control design problems in a unified framework based on polynomial optimization and its connections to the problem of moments. Contributions to the field of identification include the development of a tractable framework for robust identification of uncertain switched systems that exploits the underlying structure of the problem to substantially reduce the computational complexity and can handle both worst case and risk-adjusted descriptions. Contributions to control include a new framework for chance constrained control of uncertain switched systems that maximizes the probability of achieving a desired final state, while, at the same time, minimizing the probability of entering bad sets. As a proof-of-principle, the resulting framework is applied to the problem of designing smartphone based virtual health advisors capable of providing individualized optimal physical activity strategies.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.