Potential Well in Poincaré Recurrence

From a physical/dynamical system perspective, the potential well represents the proportional mass of points that escape the neighbourhood of a given point. In the last 20 years, several works have shown the importance of this quantity to obtain precise approximations for several recurrence time distributions in mixing stochastic processes and dynamical systems. Besides providing a review of the different scaling factors used in the literature in recurrence times, the present work contributes two new results: (1) For ϕ-mixing and ψ-mixing processes, we give a new exponential approximation for hitting and return times using the potential well as the scaling parameter. The error terms are explicit and sharp. (2) We analyse the uniform positivity of the potential well. Our results apply to processes on countable alphabets and do not assume a complete grammar.

A New Control Strategy for Bi-directional DC/DC Converter in DC Microgrid

The bi-directional DC / DC converter in DC microgrid is a typical nonlinear system which has large voltage disturbance during lead accumulator charging and discharging. In order to solve the problem of voltage disturbance, the linearization of the converter is realized by exact feedback linearization, and the sliding mode controller is designed by using exponential approximation law. The simulation results show that the method has fast response speed, strong anti-interference ability and good steady-state characteristics.

Approximation of a function describing a quality criterion of the thermo-mechanical fusible interfacing process

The present work aims to investigate the function describing the relationship between a quality criterion and input factors of the thermo-mechanical fusible /TMF/ interfacing process and to derive its effective approximation. An approximation by interpolation was applied for the purpose of the study. A numerical realization of a linear and exponential approximation of the mathematical model describing the TMF interfacing process was performed. An effective linear approximation of the function connecting the quality criterion with the input factors of the TMF interfacing process was found. This creates conditions for replacing the relatively complex function (describing the TMF interfacing process) with its linear approximation. The linear approximation gives the possibility easier and faster to determine the relationships between the input factors and the quality criterion. This created conditions for ignoring the subjective factor and for optimizing and automating the studied technological process.