State estimation and control in multi-agent decision and control systems

(Supported by NSF)
This research is concerned with the modeling, estimation and control of multi-agent systems composed of physical devices that exhibit continuous and discrete behaviors (hybrid systems). Examples include multi-robot systems for combat or surveillance applications and intelligent transportation networks subject to safety and performance constraints. In particular, my research focuses on the dynamic feedback problem for systems with continuous and discrete behavior. Partial order theory and interval abstraction are employed to mathematically characterize key quantities and to construct algorithms that keep track and control only suitable upper and lower bounds.

State Estimation on a Partial Order. The basic idea is the one of keeping track of a lower (L) and an upper (U) bound in a suitable partial order of the set of all possible states compatible with the system dynamics and with the measurements. A partial order is a set together with an ordering relation. The order is said partial when there are elements that are not comparable according to the ordering relation. In the left picture, we show with a Hasse diagram the concept of the state estimator. The prediction step of the state estimator maps forward the interval [L,U] through the system dynamics by just mapping forward the lower and the upper bound. This can be performed if the update function has order preserving properties. The correction step computes the intersection of the predicted set with a new output set. This can be simply performed in the partial order by computing the supremum of the lower bounds of the two sets and the infimum of the upper bounds. This procedure for state estimation is computationally advantageous as (1) it avoids mapping a set forward by mapping forward  each element of the set and (2) it allows to perform set intersection my just computing a supremum and an infimum between two pairs of elements.

Multi-agent Decision and Control Test-bed. Our algorithms are validated on our experimental test-bed. On the left, we show three vehicles from our multi-agent decision and control test-bed. These vehicles are equipped with on-board computer, wireless communication, positioning system, and speed sensors. A motion controller emulates the scaled longitudinal dynamics of a real vehicle including engine and transmission. The on-board computer can apply steering, throttle, and braking inputs. The dynamic response of the vehicles to these inputs is the same as the one of a full scale vehicle with automatic transmission. The test area is equipped with an ultrasound-based positioning system and it is 6 by 6 meters. The vehicles are about 30 cm long. For more information, see the lab wiki for on-going experiments.

Modular design of gene transcriptional circuits

(Supported by AFOSR)
In living organisms, huge networks of interactions (transcriptional networks) between genes and proteins play a central role in determining the functioning of the cell. Recent technological developments have set the stage for fabricating synthetic gene transcriptional networks in vivo in order to test subsystems of huge networks in isolation. This also enables us to build genetic circuitry, which can be implemented into cells to control cell behavior. Systems control theory plays a fundamental role in reasoning about design principles, modularity, and interconnections in this new type of circuits. Our research focuses on determining design principles of simple transcriptional modules, such as clocks, on determining suitable input/output descriptions of modules, and on determining the properties of the interconnections.