Research Interests - Integrative System & Control Design

I am interested in challenges around how automation and data-driven methods can be integrated into society in safe, beneficial and just ways. In my PhD and teaching activities at Berkeley, I have focused on the following aspects:

  • Data-driven methods for design, control and verification of cyber-physical energy and power systems
  • Learning & adaptation, decentralized control and privacy of networked multi-agent systems
  • Efficient methods for analysis and identification of complex dynamical systems
  • Social justice and responsibility considerations within engineering

My current research is motivated by problems in energy (intelligent operation and control of electric power distribution). Formerly, I worked with biologists on problems in cancer diagnosis and treatment (understanding heterogeneity and treatment escape in breast cancer tumors). I am interested in engineering problems that require both the rigorous modeling and analysis to exploit available domain knowledge, as well as a data-driven approach to reduce model uncertainty, adapt to new circumstances and interact with human beings. With a background in management consulting and working with public institutions, I try to come at my research problems in ways that take into account the practical context that utilities are faced with, while pushing the academic boundaries. I also find motivation in helping students understand such contexts, in order for them to be more impactful and work on engineering solutions that promote socially just outcomes.

In my research projects, I have taken an agnostic approach, trying to reason what methods could be combined and integrated to best solve a particular problem. I combine system theoretic tools (modeling, analysis, control) with optimization and data-driven inference methods (machine learning and statistics). In recent years, trends in both these research areas and their respective applications motivate exploring the intersection. On the one hand, the systems theory field has a long tradition of developing system identification tools to construct models from data. There is now a renewed interest to update these methods with new computational and inference techniques. On the other end, in statistics and machine learning, the abundance of data often leads to scalability and computational challenges, leading to the natural question of how to navigate the available data in a structured and efficient way. Therefore it is becoming more important to incorporate the domain knowledge of the application and to use modeling and abstractions to help selecting the right features and design experiments.

Selected Projects
Intelligent Infrastructures

Customized Local Differential Privacy for Multi-Agent Distributed Optimization

Collaborators: Ye Pu, Jingge Zhu, Kannan Ramchandran and Claire Tomlin

Many data-driven optimization problems may require sensitive information of participating users to calculate a solution for the overall group or network in real-time, such as in traffic or energy systems. Adversaries with access to coordination signals may potentially decode information on individual users and put user privacy at risk. Work in differential privacy so far has considered solving such problems, while protecting the privacy of user information, in a semi-distributed manner, i.e. with a central entity that computes and broadcasts certain public coordination signals to participating users. However, the lack of trust in central authorities or the lack of communication infrastructure may necessitate the full distribution of optimization algorithms, only relying on agent-to-agent communication and all calculations performed by agents. We present a fully distributed optimization algorithm that preserves local differential privacy, which is a strong notion that guarantees user privacy regardless of any auxiliary information an adversary may have. The local nature of the privacy result allows for each agent to customize its own level of differential privacy based on its needs and parameter sensitivities. We derive a sub-optimality bound as a function of the cumulative variance of the noise injected by all agents. We propose various allocation schemes to divide the maximum allowable noise, a \emph{privacy budget}, among all participating agents, either through proportional sharing or well established pricing mechanisms. Our algorithm is implemented for a distributed version of the optimal power flow problem in distribution systems to mitigate voltage variations across electric networks due to the intermittent nature of renewable generation and the variability of electric loads.

Fully Decentralized Policies for Multi-Agent Systems: An Information Theoretic Approach

Collaborators: David Fridovich-Keil and Claire Tomlin

Learning cooperative policies for multi-agent systems is often challenged by partial observability and a lack of coordination. In some settings, the structure of a problem allows a distributed solution with limited communication. Here, we consider a scenario where no communication is available, and instead we learn local policies for all agents that collectively mimic the solution to a centralized multi-agent static optimization problem. Our main contribution is an information theoretic framework based on rate distortion theory which facilitates analysis of how well the resulting fully decentralized policies are able to reconstruct the optimal solution. Moreover, this framework provides a natural extension that addresses which nodes an agent should communicate with to improve the performance of its individual policy.

Regression-based Inverter Control for Decentralized Optimal Power Flow and Voltage Regulation

Collaborators: Oscar Sondermeijer, Daniel Arnold, Tamás Keviczky and Claire Tomlin

Electronic power inverters are capable of quickly delivering reactive power to maintain customer voltages within operating tolerances and to reduce system losses in distribution grids. This paper proposes a systematic and data-driven approach to determine reactive power inverter output as a function of local measurements in a manner that obtains near optimal results. First, we use a network model and historic load and generation data and do optimal power flow to compute globally optimal reactive power injections for all controllable inverters in the network. Subsequently, we use regression to find a function for each inverter that maps its local historical data to an approximation of its optimal reactive power injection. The resulting functions then serve as decentralized controllers in the participating inverters to predict the optimal injection based on a new local measurements. The method achieves near-optimal results when performing voltage- and capacity-constrained loss minimization and voltage flattening, and allows for an efficient volt-VAR optimization (VVO) scheme in which legacy control equipment collaborates with existing inverters to facilitate safe operation of distribution networks with higher levels of distributed generation.

Real-Time Distribution Grid State Estimation with Limited Sensors and Load Forecasting

Collaborators: Daniel Arnold, Duncan Callaway and Claire Tomlin

High penetration levels of distributed generation (DG) and electric vehicles (EVs) diversify power flow and bring uncertainty to distribution networks, making planning and control more involved for distribution system operators (DSOs). The consequent need to augment forecasts with real-time state estimation is economically and technically challenging since it requires investing in a large number of sensors and these have to communicate with an often older and slower supervisory control and data acquisition (SCADA) systems. We address distribution grid state estimation via combining only a limited set of sensors with load forecast information. It revisits open problems in a recent paper that proposes a Bayesian estimation scheme. We derive the estimator for balanced power networks via rigorous modeling, allowing for generalization to three phase unbalanced networks. An offline analysis of load aggregation, forecast accuracy and number of sensors provides concrete engineering trade-offs to determine the optimal number of sensors for a desired accuracy. This estimation procedure can be used in real time as an observer for control problems or offline for planning purposes to asses the effect of DG or EVs on specific network components.

Cancer Systems Biology

Heterogeneity in cancer dynamics: A convex formulation to dissect dynamic trajectories and infer LTV models of networked systems

Collaborators: Young-Hwan Chang, Stephan Liu, Jim Korkola, Joe Gray and Claire Tomlin

Breast cancer tumors have inherently heterogeneous cell types that respond differently to treatments. Although there is a wealth of studies describing canonical cell signaling networks, little is known about how these networks operate in different cancer cells and treatments. This paper proposes a method to split a set of responses gathered from experiments on different cancer cells up into common and specific components. The key to this retrieval is the derivation of a linear time-varying model of the shared dynamics among the different cell lines. A convex optimization problem is derived that retrieves both the model and the common and specific responses without a priori information. The method is tested on synthetic data, and verifies known facts when tested on a biological data set with protein expression data from breast cancer experiments. The technique can be used to analyze specific responses to understand what treatments can be combined to persistently treat a heterogeneous cancer tumor. The linear time-varying model sheds light on how proteins interact over time.

A Linear Time-invariant Model of Phenotype Dynamics in Cancer Cell Populations

Collaborators: Margaret Chapman (lead), Tyler Risom, Rosalie Sears and Claire Tomlin

Phenotypic heterogeneity, or cellular diversity on the phenotypic level, poses a major hurdle to effective treatment of certain cancers (e.g., triple negative breast cancer). Hence, the discovery of strategies to reduce this heterogeneity is a fundamental priority for the cancer biology community. Knowledge of the phenomena that govern drug-induced cell populations is needed to design therapeutic approaches that systematically control phenotypic diversity. In this work, we present a mathematically simple, yet powerful framework to suggest why observed trends in phenotype time-trajectories occur and why trends may change under application of targeted therapies. A linear time-invariant model is derived to represent cell division and death of each phenotype in addition to switching between phenotype pairs. A convex optimization procedure is formulated and solved to estimate values of model parameters using measurements from a breast cancer cell line. The resulting values are analyzed and found to agree qualitatively with several existing biological hypotheses. Remarkably, the model indicates that the PI3K/mTOR inhibitor therapy reduces the prominence of basal phenotypes due to switching behavior and low cell division, as opposed to other logical explanations, such as selective elimination. Further, the model suggests that the MEK inhibitor drug promotes the prominence of basal phenotypes via switching phenomena, instead of increased cell division or reduced death. Our modeling framework and initial results are important milestones in the design of richer models and experiments with the potential to drive discovery of effective cancer treatments.