We deal with a control problem for a complex social network in which each agent has an action and an opinion, evolving according to a coevolutionary model. In particular, we consider a scenario in which a committed minority —a set of stubborn nodes— aims to steer a population, initially at a consensus, to a different consensus state. Our study focuses on determining the conditions under which such a goal is reached, and ultimately, how to optimally define a minimal committed minority. First, we derive a general monotone convergence result for the controlled coevolutionary model, under mild and general assumptions on the agents’ revision sequence. Then, we build on our theoretical result to propose a systematic approach to investigate the research problem.