Fractional Calculus
Automatic control is a branch of scientific research that deals, among other things, with automatons. In our daily lives, we keep surrounded by automated systems, such as battery chargers, cruise control mechanisms in cars, automatic pilots for aircrafts and rockets, and so on. These dynamic systems require continuous control to ensure that their function in question is maintained. Engineers in automatic control work in the fields of domestic appliances, automobiles, aerospace, chemical process, wastewater management, 3D printers and so on.
Fractional calculus is used to add up new solutions to the problematics presented in automation, but considering the basiest case: The linear systems case. This case, even though considered as “mature”, enable us to find new possibilities due to the generalization of calculus definitions of integrals and derivatives to the real or even complex order case.
Fractional calculus will be used in this work as a tool to design a control feedback algorithm for linear fractional and non fractional order, time-invariant systems with time-delay and as a mathematical modeling tool for large-scale mechanical systems.
My works on Fractional Calculus
Parameter estimation of fractional order systems combining genetic algorithms and extended fractional Kalman filter. A.-J. Guel-Cortez and Eun-jin Kim. Submitted to 24th International Symposium on Mathematical Theory of Networks and Systems. Received February 3, 2020.
PD mu controller applied to a robotic teleoperated system.
Interesting talks about FC
Mamikon Gulian on Fractional Calculus & Hidden Physics
Mamikon Gulian talks about his research using machine learning and fractional calculus in a talk titled, “Discovering Physics with Machine Learning: Fractional Calculus and Beyond.” Mamikon Gulian is a doctoral candidate in Mathematics, with focus on Applied Mathematics at Brown University. This talk was part of Research Matters, featuring short talks about research by Brown University Graduate Students on November 4, 2017. For more information, please visit: http://www.brown.edu/go/researchmatters
Fractional calculus helps control systems hit their mark
Read the article: http://dx.doi.org/10.1109/JAS.2016.75... Padula and Visioli "Set-point Filter Design for a Two-degree-of-freedom Fractional Control System.” IEEE/CAA Journal of Automatica Sinica (2016). doi: 10.1109/JAS.2016.7510100. This work has been partially supported by the Australian Research Council (DP160104994). Video produced by https://www.researchsquare.com
Fractional Calculus ~ (FC1) An Introduction
In this video, we briefly review the power rule for the classical derivative from elementary calculus and pose the question of calculating fractional order derivatives of functions. We generalize the power rule of power functions to arbitrary orders and extend it to allow non-integer values for the derivative order.