System identification based on physical laws often involves parameter estimation. Even if parameters are theoretically identifiable, they may be poorly estimable for a given experiment. Thus a significant increase in accuracy of the parameter estimation may be obtained by a suitable choice of experimental conditions. The original idea of this paper is the combination of a dynamical programming method with a gradient algorithm in the solution of the optimal design. After getting an optimal input, the parameter estimation is performed by minimizing a weighted least square criterion. Weights are either based on the known measurement noise or given by the solution of a linear matrix inequality problem.