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?Comment: This is a journal version of the extended abstract arXiv:1707.02058 which appeared in Concur 2017, together with proofs

@article{paperbot779,
  title = {Controlling a population},
  author = {Nathalie Bertrand and Miheer Dewaskar and Blaise Genest and Hugo Gimbert and Adwait Amit Godbole},
  journal = {Logical Methods in Computer Science},
  volume = {Volume 15, Issue 3},
  year = {2019},
  doi = {10.23638/lmcs-15(3:6)2019}
}