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

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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.