Controlling a population

TL;DR

This paper studies a uniform control problem for a population of identical agents modeled by finite automata, aiming to synchronize all agents to a target state regardless of their non-deterministic reactions, using a game-theoretic framework.

Contribution

It introduces a new population control setting inspired by biological systems, modeling it as a parameterized game and analyzing the control problem for all population sizes.

Findings

Formulation of the population control problem as a 2-player game.

Analysis of the control problem's decidability and complexity.

Development of algorithms for controlling populations across all sizes.

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?