Modelling of one-dimensional noisy dynamical systems with a Frobenius-Perron solution

Energy storage plays an important role in maintaining energy balance for the future power network. A novel solution by learning human body energy system is explored aiming to determine the best ratio between the energy storage and generation capacity with variations of mixed energy sources. The fluctuation process of energy storage in human body and power network can be approximately represented by a one-dimensional noisy dynamical system. This paper develops a new approach to inferring a piecewise linear semi-Markov transformation of a one-dimensional discrete time dynamical system that is subjected to additive stochastic noise, based on sequences of probability density functions observed from the noisy dynamical system. The reconstructed map that approximates the underlying transformation can be used to predict the amount of stable fat/energy storage, and to achieve the bio-inspired three-point (generation, load and storage) balance structure. A numerical example is used to demonstrate the applicability of the derived algorithm and robustness with respect to additive stochastic noise.