Title: Controlling a population,
Abstract: We introduce a new setting where a population of agents, each modelled by a
finite-state system, are controlled uniformly: the controller applies the same
action to every agent. The framework is largely inspired by the control of a
biological system, namely a population of yeasts, where the controller may only
change the environment common to all cells. We study a synchronisation problem
for such populations: no matter how individual agents react to the actions of
the controller, the controller aims at driving all agents synchronously to a
target state. The agents are naturally represented by a non-deterministic
finite state automaton (NFA), the same for every agent, and the whole system is
encoded as a 2-player game. The first player (Controller) chooses actions, and
the second player (Agents) resolves non-determinism for each agent. The game
with m agents is called the m -population game. This gives rise to a
parameterized control problem (where control refers to 2 player games), namely
the population control problem: can Controller control the m-population game
for all m in N whatever Agents does?