Naturalistic systems are systems of natural origin that are subject to human intervention and fundamental to the quality of life on earth, such as environmental or biological systems. Managing these systems is challenging because the underlying models are unknown, or are high-dimensional, and large time series data sets are usually not available. So far, I have focused on building dynamic models and developing control-theoretic tools to manage cancer cell populations and storm water conveyance networks in the presence of real-word uncertainties.
Modeling & Analysis of Triple-Negative Breast Cancer via Switched Dynamical Systems (with T. Risom, E. Langer, A. Aswani, E. Mazumdar, R. Sears, C. Tomlin)
We have built dynamic models of the interactions between cells expressing different phenotypes, or sets of observable traits, using data from a Triple-Negative breast cancer cell line. From these models, we can infer the transitions that occur between cells of different phenotypes in response to anti-cancer therapy, which is important because such behaviors facilitate the onset of drug resistance. We are also developing new theory on uncertainty in therapeutic response models to guide the design of drug schedules in practice. It is not possible to test all drug schedules in the laboratory, and theoretical work has the potential to identify which kinds of tests would be more useful. Relevant publications are listed here.
Risk-Sensitive Reachability Analysis as a Design Tool for Stormwater Systems (with K. Smith, D. Freyberg, J. Fisac, S. Jha, S. Singh, M. Chen, D. Sedlak, C. Tomlin)
Modern stormwater systems are designed to satisfy performance criteria under a restricted collection of artificial events in part because weather is inherently hard to predict. As recent circumstances suggest (e.g., California drought, Texas floods), standard design practices do not properly account for rainfall uncertainty or rapid urbanization, both of which greatly influence the performance and safety of stormwater infrastructure. To measure system robustness objectively in the presence of precipitation uncertainty, we are developing a control-theoretic method, called risk-sensitive reachability analysis. We see risk-sensitive reachability as a tool to evaluate candidate designs (e.g., green infrastructure, outlet sizing, or active controllers) in a cost-effective way that appreciates uncertainty and risk. This will be the first time that reachability theory is applied to the stormwater sector. In addition, the incorporation of risk-sensitivity into reachability analysis is a new theoretical contribution.