Research Areas

Existing computational tools for control and verification do not scale to complex systems with many interconnected components, and learning and decision making capabilities. To manage this complexity we are developing compositional and hierarchical design and verification methods that break apart intractably large problems into subproblems of manageable size. The aim in compositional analysis is to expose a complex system as an interconnection of smaller subsystems and to derive system-level guarantees from subsystem properties. The aim in hierarchical control is to decompose the synthesis and verification tasks into layers, from high-level decision making to low-level control synthesis. In prior work we have combined these approaches for stability and performance guarantees. We are now addressing richer classes of specifications, such as those expressed as automata or in temporal logic, and exploiting tools from statistical learning to provide probabilistic guarantees.

Multi-agent control systems (e.g., coordinated fleets of unmanned aircraft or autonomous automobiles, satellite mega-constellations, integrated defense systems) enable applications with complex objectives and constraints that are not possible using individual systems. Among other problems, we are studying multi-interceptor systems that guard assets from multiple threats. We formulate and efficiently solve assignment problems where interceptors are optimally assigned to threats, and design learning-based algorithms that select the best real-time actions for interceptors in the presence of environmental disturbances and system uncertainty. Furthermore, we are exploring design methods to automatically tune each interceptor’s flight control system to achieve guaranteed performance towards the overarching multibody system objective. We test the results on 6-DOF airframe models and state-of-the-practice intercept guidance laws and autopilot algorithms.

Connected vehicles and infrastructure, combined with increased automation, promise to minimize congestion, enhance safety, and lower emissions. We are pursuing a hierarchical traffic control framework that integrates feedback strategies at the vehicle, road link, and network layers. In particular, at the vehicle layer we are investigating how forming platoons can increase traffic throughput in urban roads and intersections. Further work focuses on platoon formation on highways, with the goal of improving travel time by optimally assigning vehicles to platoons traveling in a dedicated lane. In other recent work we have brought tools from formal methods to develop controllers that ensure that the traffic flow satisfies high-level objectives expressed in temporal logic. The resulting models and algorithms are field tested using sensor measurements 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 among neighboring cells as well as between cells and the environment. Our research reveals theoretical conditions for spontaneous pattern emergence, as well as new perspectives for understanding how initial patterns are refined into later patterns. In recent work, we collaborated with experimental biologists to empirically demonstrate spontaneous contrasting patterning in systems of genetically engineered microorganisms, including colonies of bacteria communicating through diffusible molecules, as well as engineered yeast cells interacting by way of a computer-controlled light input. Currently, we are investigating applications of networked systems theory to the dynamics of pattern formation, with particular interest in understanding how spatial variation in gene expression evolves over time in developing embryos. Our research provides insight into natural biological mechanisms and lays the groundwork for designing synthetic biological systems to achieve more complex behaviors.