Broadcast feedback control of cell populations using stochastic Lyapunov functions with application to angiogenesis regulation

This paper introduces a broadcast feedback approach to controlling the aggregate behavior of a population of cells. Control of the angiogenesis process, which is known to exhibit stochastic behavior, is the target application. A simple model is considered that assumes a cloud of independent cells that need to be controlled to a specific location or along a trajectory. Each cell makes a random decision to move to the right, to the left, or remain in its current location at each time step. Additionally, each cell has a unit time refractory period after a movement during which it cannot move again. Because the cells live in a "wet" environment, it is not feasible to control their behavior independently. Instead, the system output is the centroid of the cloud, and the controller uses the error between the output and the reference to broadcast a single probability of transitioning to the ensemble of cells. Conditions for stability in the output are obtained using a stochastic Lyapunov function. An analysis of the dispersion of the cloud of cells is given. Additional intercellular regulatory behavior is added to better represent a real system and leads to a method of variance control under some additional assumptions. Simulation verifies the theoretical results and affirms that aggregate output can be stably controlled to a reference or along a trajectory.