Abstract In this work, model-predictive control (MPC) was combined for the first time with singular perturbation theory, and an original plasma kinetic control method based on extremely simple data-driven models and a two-time-scale MPC algorithm has been developed. A comprehensive review is presented in this paper. Slow and fast semi-empirical models are identified from data, by considering the fast kinetic plasma dynamics as a singular perturbation of a quasi-static equilibrium, which itself is governed, on the slow time scale, by the flux diffusion equation. This control technique takes advantage of the large ratio between the time scales involved in magnetic and kinetic plasma transport. It is applied here to the simultaneous control of the safety factor profile, q(x), and of several kinetic variables, such as the poloidal beta parameter, βp, and the internal inductance parameter, li, on the EAST tokamak. In the experiments, the available control actuators were lower hybrid current drive (LHCD) and co-current neutral beam injection (NBI) from different sources. Ion cyclotron resonant heating (ICRH) and electron cyclotron resonant heating (ECRH) are used as additional actuators in control simulations. In the controller design, an observer provides, in real time, an estimate of the system states and of the mismatch between measured and predicted outputs, which ensures robustness to model errors and offset-free control. A number of control applications are described in the paper, either in nonlinear simulations with EAST-like parameters or in real experiments on EAST. Various controller configurations were tested, with up to three controlled variables chosen among q0 = q(x=0), q1 = q(x=0.5), βp and li. Both the extensive nonlinear simulations and the experiments described in this paper have demonstrated the relevance of combining model-predictive control, data-driven models and singular perturbation methods for plasma kinetic control.