Research Areas

Existing computational tools for control synthesis and verification do not scale to today's increasingly complex systems with many interconnected components. We are developing compositional and hierarchical design and verification methods to manage this complexity and to break apart an intractably large problem into subproblems of manageable size. The aim in compositional design is to expose a complex system as an interconnection of smaller subsystems and to derive guarantees for each subsystem under appropriate assumptions on the others. The aim in hierarchical control is to compose a control action for an aggregate model and to refine this action to lower-level controllers. In prior work we have developed methods to obtain stability and performance guarantees in a scalable fashion; we are now addressing richer classes of specifications, such as those expressed in temporal logic, and finite-time robustness objectives in the presence of uncertainty. For further computational savings we exploit sparsity and sign patterns, as well as symmetries in system models.

Connected vehicles and infrastructure, combined with increased automation, promise to minimize congestion, enhance safety, and lower emissions. We are pursuing a comprehensive traffic control framework that integrates feedback strategies at the the vehicle, road link, and network layers. Control in the vehicle layer comprises speed/lane adjustments as well as autonomy features, such as platoon formation. Control in the road link layer involves adapting signal timing and lane allocation to current traffic conditions. Control in the network layer includes demand management with information dissemination. In our recent work we have brought tools from formal methods to develop controllers that ensure traffic flow satifies high-level objectives expressed in temporal logic. In a separate project with Alex Kurzhanskiy, Pravin Varaiya, and Roberto Horowitz, we aim to use heterogeneous sensors and large-scale data collection to integrate information from all layers into a coordinated control scheme. The resulting models and algorithms are field tested using sensor measurement and signal timing data.

We are investigating how spatial patterns in gene expression emerge in multicellular systems, both real and synthetic. Such biological systems are typically high dimensional and nonlinear, involving interactions between neighboring cells as well as between cells and the environment. Patterns may emerge spontaneously from random initial conditions or through refinement of existing prepatterns. In collaboration with the Arkin lab, we have theoretically characterized and experimentally demonstrated spontaneous contrasting patterning in adjacent colonies of synthetically engineered bacteria that inhibit their neighbors through diffusible signaling molecules. We also recently proposed a spatial filtering framework to analyze prepattern processing in networks of interacting cells, with applications to understanding how distinct cell types emerge in developing embryos. Currently, we are probing the role of molecular-level stochasticity on cellular-level patterning. Our research into predicting pattern formation provides insight into natural biological mechanisms and lays the groundwork for designing synthetic biological systems to achieve more complex behaviors.