Research Areas

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 challenging tasks such as environmental monitoring, target localization, 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 agents for provably stable design of cooperative control systems. Passivity is an abstraction of energy conservation and dissipation in physical systems, and is inherent in Lagrangian and Hamiltonian models commonly used for robots, satellites, etc. The passivity methodology is thus applicable to complex agent models and offers ample design flexibility for robust and adaptive algorithms. We have developed such algorithms for numerous tasks, including formation stabilization, gradient climbing, and synchronized path-following. One of the current research topics is to design distributed control strategies for formation control of a team of mobile agents that allows for size-scaling of the formation while maintaining the formation shape. Another current direction is designing communication graphs via convex optimization techniques to meet prescribed robustness and performance bounds.

We investigate the interplay between the structure of biological networks and their spatial and temporal dynamical behavior. A deep understanding of this interplay is essential not only for the analysis of existing systems, but also for the design of novel synthetic networks. We have thus far investigated cyclical interconnection structures that are commonly found in biological oscillators, and developed control-theoretic criteria to predict oscillations or convergence to steady-states. We are currently studying other recurrent structures and, in addition, identifying novel synthetic networks for prescribed dynamical behaviors. One such research direction, 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 gene networks that have the ability to generate patterns with a robust set of parameters. Our investigations have led to a new a class of networks that we call “quenched oscillator” systems. These systems consist of a primary feedback loop that serves as an oscillator, and a secondary feedback loop that quenches the oscillations and incorporates a diffusible molecule. Diffusion releases the quenching effect in higher spatial frequencies, thus generating patterns.

By abstracting the common core of our results for cooperative control systems, communication networks, and biological systems, we are now developing a broadly applicable methodology that employs control-theoretic input-output concepts. This methodology overcomes the complexity of the network by dividing the design and analysis into two levels: At the network level, we represent the components with appropriate input-output properties as abstractions of their complex dynamical models. At the component level, we study the individual dynamical models and verify or assign the desired input-output properties without relying on further knowledge of the interconnection. The proposed methodology is neither a “top-down” approach that overrides the inherent features of the components, nor a “bottom-up” strategy that studies the components in isolation and fails to reveal emergent network behaviors. Instead, it combines the desirable elements of each approach, and employs input-output properties as carriers of information between network- and component-level analyses. Current research topics include the certification of desirable input-output properties for component models using analytical and numerical techniques, the generalization of the input-output framework to stochastic models and to systems with time delays, and applications to distributed optimization problems.