Research Areas

Distributed Control of Multi-Agent Systems

Networked Satellites 

Multiple robots or sensors have a number of advantages over a single agent, including robustness to failures of individual agents, reconfigurability, and the ability to perform tasks such as environmental monitoring, target localization, and space interferometry that cannot be achieved by a single agent. Agents possess a mix of communication and sensing capabilities, and perform cooperative tasks via distributed control algorithms. Our research has led to a systematic methodology that makes use of passivity properties of the agents for provably stable design of cooperative control systems. Passivity is an abstraction of energy conservation and dissipation in dynamical systems, and is inherent in Lagrangian and Hamiltonian models commonly used for robots, satellites, etc. By exploiting passivity properties of the agents, we have developed robust and adaptive distributed algorithms for numerous team tasks, including formation stabilization, gradient climbing, and synchronized path-following. One of the current research tasks is to design switching rules between multiple modes of agent operation within a team to achieve stringent safety and performance goals. In a collaborative project with the Norwegian University of Science and Technology, we are applying our results to the development guidance, navigation and control algorithms for monitoring of coastal and marine environments with mobile, autonomous sensor platforms.

Analysis and Synthesis of Biomolecular Networks

Biomolecular Network 

We investigate the interplay between the structure of biological networks and their spatial and temporal dynamical behavior. This study is not only essential for understanding natural systems; it also enables the design of novel synthetic networks that exhibit prescribed dynamical behaviors. One of our current research topics, pursued in collaboration with the Maharbiz and Arkin groups, is designing networks that generate spatial patterns of gene expression. Motivated by naturally occurring developmental processes where specific genes are activated in specific regions in the embryo, our goal is to design synthetic gene networks that have the ability to generate patterns with a robust set of parameters. Our investigations have led to a “quenched oscillator” network that combines an oscillator subsystem with a feedback loop that quenches the oscillations and contains a diffusible molecule for cell-to-cell communication. Diffusion releases the quenching effect in higher spatial frequencies and generates spatio-temporal patterns. We are also pursuing a contact-mediated signaling mechanism as an alternative to diffusion-driven patterning. We have developed an efficient mathematical approach to predict and design patterns with this mechanism and we are now leveraging the results to engineer a programmable multicellular patterning system.

An Input-Output Approach to Networks

Input Out Approach 

By abstracting the common core of our results for several types of networks, we are developing a broad methodology that employs control-theoretic input-output concepts to predict and engineer collective behavior. This approach overcomes the complexity of the large scale, nonlinear dynamical model by dividing the analysis and design tasks into two layers: At the network layer, we represent the nodes with input-output properties as abstractions of their detailed models and exploit these properties together with the interconnection structure to ascertain desirable behaviors, such as stability, synchronization, and spatial pattern formation. At the node layer, we verify or assign the input-output properties using analytical and numerical techniques that do not rely on knowledge of global network properties. The proposed methodology is neither a “top-down” approach that ignores inherent features of the components, nor a “bottom-up” strategy that fails to reveal emergent network behaviors. Instead, it identifies key properties of the components and their interconnection structure that determine the ensemble behavior. Current research topics include the generalization of the input-output framework to stochastic systems, spatially distributed models, and to systems with time delays. Another research task is to enable real-time adaptation of network connectivity by updating link weights with distributed algorithms.