Particle-based Gaussian process optimization for input design in   nonlinear dynamical models
  We propose a novel approach to input design for identification of nonlinear state space models. The optimal input sequence is obtained by maximizing a scalar cost function of the Fisher information matrix. Since the Fisher information matrix is unavailable in closed form, it is estimated using particle methods. In addition, we make use of Gaussian process optimization to find the optimal input and to mitigate the problem of a large computational cost incurred by the particle filter, as the method reduces the number of functional evaluations. Numerical examples are provided to illustrate the performance of the resulting algorithm. 
Patricio E. Valenzuela, Johan Dahlin, Cristian R. Rojas and Thomas B.   Sch\"on
math.OC