Solving the inverse Frobenius-Perron problem using stationary densities of dynamical systems with input perturbations

Stationary density functions statistically characterize the stabilized behavior of dynamical systems. Instead of temporal sequences of data, stationary densities are observed to determine the unknown transformations, which is called the inverse Frobenius-Perron problem. This paper proposes a new approach to determining the unique map from stationary densities generated by a one-dimensional discrete-time dynamical system driven by an external control input, given the input density functions that are linearly independent. A numerical simulation example is used to validate the effectiveness of the developed approach.