This paper proposes an indirect adaptive control method based on recurrent neural networks. To achieve satisfactory closed-loop performances, a neural emulator (NE) and a neural controller (NC) adapting rates are established using the multiobjective particle swarm optimization (MOPSO) algorithm. The proposed MOPSO algorithm has been designed to minimize, simultaneously, two separated objective functions: the emulation and the tracking errors. The proposed approach guarantees that the NE tracks the system dynamics within a short time window. Consequently, it provides for the suggested control structure useful information to synthesize optimal adaptive rates of the NE and NC. To validate the effectiveness of the proposed MOPSO algorithm, a numerical example and an experimental validation on a chemical reactor are proposed.