# Research Interests

Trustworthy autonomy; safety analysis

Risk measure theory and analysis

Blending methods in learning and control

Breast cancer modeling and treatment design

Design and control of societal-scale urban infrastructure systems (e.g., food-energy-water)

# Research Vision

Develop quantitative decision support tools for more

**trustworthy autonomy**by leveraging systems & reinforcement learning theory, risk measures, data analysis, and realistic assumptions about uncertainties to better protect against rare harmful outcomes; andTransfer these tools to address challenges in

**smart cities**and**healthcare**, including the need for more sustainable control of food-energy-water systems and cancer systems.

Next, I summarize my exciting current research projects and future plans.

# Risk-Sensitive Safety Analysis

An important problem is to quantify how safe a dynamic system can be despite real-world uncertainties and to synthesize control policies that ensure safe operation. Existing approaches typically assume either a worst-case perspective (which can yield conservative solutions) or a risk-neutral perspective (which neglects rare events). An improved approach would seek a middle ground that allows practitioners to modify the assumed level of conservativeness as needed. To this end, we have developed a new risk-sensitive approach to safety analysis that facilitates a tunable balance between the worst-case and risk-neutral perspectives by leveraging the** Conditional Value-at-Risk** (CVaR) measure. This work proposes **risk-sensitive safety specifications** for stochastic systems that penalize one-sided tail risk of the cost incurred by the system’s state trajectory. The theoretical contributions have been to prove that the safety specifications can be under-approximated by the solution to a **CVaR-Markov decision process**, and to prove that a value iteration algorithm solves the reduced problem and enables tractable **risk-sensitive policy synthesis** for a class of linear systems. A key empirical contribution has been to show that the approach can be applied to non-linear systems by developing a realistic numerical example of an urban water system. The water system and a thermostatically controlled load system have been used to compare the CVaR criterion to the standard risk-sensitive criterion that penalizes mean-variance (exponential disutility). Numerical experiments demonstrate that reducing the mean and variance is not guaranteed to minimize the mean of the more harmful cost realizations. Fortunately, however, the CVaR criterion ensures that this **safety-critical tail risk** will be minimized, if the cost distribution is continuous.

**Papers**: Chapman et al., *American Control Conference*, 2019 PDF; Chapman et al., under review for *IEEE Transactions on Automatic Control *PDF*.*

**Collaborators**: Marco Pavone (Stanford), Kevin Smith (Tufts), Insoon Yang (Seoul National), Jonathan Lacotte (Stanford), Susmit Jha (SRI), Yuxi Han (Wisconsin-Madison), and Claire Tomlin.

# Resilient Design of Urban Water Infrastructure Systems

Modern stormwater systems are designed to satisfy safety and performance criteria under a restricted set of artificial scenarios since weather is hard to predict and public funding is limited. As recent historical events (e.g., Houston flooding) suggest, standard design practices do not properly account for rainfall uncertainty, rapid urbanization, or rare extreme storms. We have been working with the **Berkeley Water Center **through Re-Inventing the Nation's Urban Water Infrastructure (ReNUWIt)** **NSF Engineering Research Center to develop improved design practices. We see risk-sensitive safety analysis as a tool to evaluate candidate designs (e.g., green infrastructure, outlet sizing, or active controllers) in a realistic way that accounts for dynamic coupling between system nodes and low-probability high-consequence outcomes. Our project **Unclogging the DRAIN: Designing Robust Autonomous Infrastructure Networks **was featured in the September 2019 ReNUWIt Industry Newsletter.

**Papers**: Chapman et al., *IEEE Conference on Technologies for Sustainability*, 2018 PDF; Chapman et al., under review for *IEEE Transactions on Automatic Control *PDF*.*

**Collaborators**: Kevin Smith (Tufts), David Freyberg (Stanford), and Claire Tomlin.

**Posters**: 2019 ReNUWIt Annual Meeting; 2018 AGU Fall Meeting (presented with K. Smith).

# Breast Cancer as a Safety-Critical System

Triple-negative breast cancer (TNBC) is an especially aggressive and deadly form of breast cancer that disproportionately affects younger women or women of African descent. This cancer is difficult to treat, since it lacks the three most common proteins in breast cancer and is phenotypically diverse. After treatment with certain targeted therapies, surviving TNBC cells become resistant to future treatment and their phenotypic traits change (*Nature Comm* paper). A set of phenotypic traits that is associated with specific cellular behaviors is called a **phenotypic state**. We have developed **data-driven models** of phenotypic state dynamics to help discover why TNBC cells can survive despite treatment with certain therapies. By applying **statistical learning** methods, we have found that changes in phenotypic state transition rates enhance the survival of basal cells following Trametinib therapy (PLoS Comp. Biol. paper). That is, TNBC can escape from this therapy in part by transitioning to the basal state.

In addition to providing important scientific insights, this work has motivated the need for quantitative decision support tools based on **systems theory** and **data analysis** to guide the process of designing **therapeutic treatment schedules**. (Indeed, it is impossible to test all therapeutic schedules in the laboratory, and it is hard to find tolerable drugs that manage particular phenotypic states.) Thus far, we have proposed a class of therapeutic schedules with tolerability specifications and have derived sufficient mathematical conditions for the decay of cancer cell populations under this class through switched systems analysis (CDC 2018). My talk at the **NCI Physical Sciences Oncology Network & Cancer Systems Biology Consortium** 2019 MathBio Meeting summarizes our research on the drug scheduling problem so far (slides).

**Papers**: Risom et al., *Nature Communications*, 2018 PDF; Chapman et al., *PLoS Computational Biology*, 2019 PDF; Chapman et al., *Conference on Decision & Control*, 2018 PDF; Chapman et al., *Conference on Decision & Control*, 2016 PDF.

**Collaborators**: Tyler Risom (Stanford), Ellen Langer (OHSU), Megan Turnidge (OHSU), Anil Aswani, Eric Mazumdar, Rosalie Sears (OHSU), Joe Gray (OHSU), and Claire Tomlin.

# Future Research Directions

**Combine methods in learning and control**to incentivize human behavior towards enhancing the sustainability of societal-scale urban infrastructure systems.Adapt risk-sensitive safety analysis to optimize therapeutic cancer treatment schedules, as more data for characterizing uncertainties in cancer systems becomes available.

Extend methods in

**optimal control**and**reinforcement learning**to a**risk-sensitive perspective**by using coherent risk measures to assess costs.Tractably evaluate which regions within PG&E’s service area are more

**prone to fire risk**and thus require the installation of underground power lines.Develop trustworthy algorithms that recommend more

**tolerable patient-specific strategies**for treating triple-negative breast cancer.

Last updated: 10/27/2019