Real-time simultaneous control of several radially distributed magnetic and kinetic plasma parameters is being investigated on JET, in view of developing integrated control of advanced tokamak scenarios. This paper describes the new model-based profile controller which has been implemented during the 2006-2007 experimental campaigns. The controller aims to use the combination of Heating and Current Drive (H&CD) systems - and optionally the Poloidal Field (PF) system - in an optimal way to regulate the evolution of plasma parameter profiles such as the safety factor, q(x), and gyro-normalized temperature gradient, ρTe*(x). In the first part of the paper, a technique for the experimental identification of a minimal dynamic plasma model is described, taking into account the physical structure and couplings of the transport equations, but making no quantitative assumptions on the transport coefficients or on their dependences. To cope with the high dimensionality of the state space and the large ratio between the time scales involved, the model identification procedure and the controller design both make use of the theory of singularly perturbed systems by means of a multiple-time-scale approximation. The second part of the paper provides the theoretical basis for the controller design. The profile controller is articulated around two composite feedback loops operating on the magnetic and kinetic time scales, respectively, and supplemented by a feedforward compensation of density variations. For any chosen set of target profiles, the closest coherent state achievable with the available actuators is uniquely defined. It is reached, with no steady state offset, through a near-optimal proportional-integral control algorithm. Conventional optimal control is recovered in the limiting case where the ratio of the plasma confinement time to the resistive diffusion time tends to zero. Closed-loop simulations of the controller response have been performed in preparation for experiments, and typical results are shown. Finally, in the last section of the paper, the first experimental results using this dynamic-model approach to control the plasma current and the safety factor profile on JET, either with the three H&CD systems or also with the PF system as an additional actuator, are presented and discussed.