Collaborative Research: Data driven control of switched systems with applications to human behavioral modification

急剧上升的医疗保健成本威胁着国家经济。其中80%以上的费用是由慢性病造成的，慢性病可以通过改变生活方式来预防或减轻。体力活动也是理想的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。在这些观察的激励下，这项建议寻求开发一个易于处理的、实用的框架，以设计个性化的行为监控系统，旨在保持最佳的体力活动水平。这是通过将问题嵌入到一个更一般的系统理论问题中来实现的：为以模型集合为特征的系统设计具有可证明性能的控制器，其中模型的数量和参数都不是先验已知的，必须从从多个质量差异较大的传感器收集的实验数据中获得。教育积极融入该项目，首先是针对城市中学生的数据驱动建模的STEM夏令营项目，然后是大学层面的多学科项目，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，这些活动与招聘工作相辅相成，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，扩大代表不足的群体参与研究的范围。在设计有效的行为干预问题的基础上，该方案寻求开发一个综合的、易于计算的框架，用于综合由切换差分包含描述的一类系统的数据驱动控制律。这些模型出现在广泛的领域，从弹性基础设施到医疗保健，具有大量不确定性和突然变化的动态。该研究基于多项式优化及其与矩问题的联系，在统一的框架内解决了辨识和控制设计问题。对辨识领域的贡献包括开发用于不确定切换系统的稳健辨识的易处理框架，该框架利用问题的底层结构来显著降低计算复杂性，并且可以处理最坏情况和经风险调整的描述。对控制的贡献包括一种用于不确定切换系统的机会约束控制的新框架，该框架最大化达到期望的最终状态的概率，同时最小化进入坏集的概率。作为原则证明，所产生的框架被应用于基于智能手机的虚拟健康顾问的设计问题，该虚拟健康顾问能够提供个性化的最佳身体活动策略。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.