DIFFERENTIAL EQUATIONS, DIFFERENCE EQUATIONS AND FUZZY LOGIC IN CONTROL OF DYNAMIC SYSTEMS
Abstract
In this article, the use of certain mathematical tools to create a dynamic system control is described; such a control could be applied to a power supply system. In continuous dynamic systems, the control of the system is described by one or more differential equations; however, in discrete dynamic systems, this control is described by one or more difference equations. Both differential and difference equations are highly effective tools in conventional mathematical analysis. In the previous twenty years, algorithmic principles of fuzzy logic in the control of the dynamic systems have been very useful. In this article, the applications of all three approaches are presented. In the case of the fuzzy logic approach, there is an example of the energy efficiency in the employment of biomass with an emphasis on developing the environmental sustainable biomass index.
Downloads
References
E. Kreyszig: Advanced Engineering Mathematics, John Wiley & Sons, Inc., New York, 1999
T.M. Guerra, A. Sala, K. Tanaka: Fuzzy control turns 50: 10 years later, Fuzzy sets and systems 281, pp. 168‐182, 2015
J. J. Buckley, T. Feuring: Fuzzy differential equations, Fuzzy sets and systems 110, pp. 43‐ 54, 2000
A. Khastan, R. Rodriguez‐Lopez: On the solution to first order linear fuzzy differential equations, Fuzzy Sets and Systems 295, pp. 114‐135, 2016
D. Qui, W. Zhang, C. Lu: On fuzzy differential equations in the quotient space of fuzzy numbers, Fuzzy sets and systems 295, pp. 72‐98, 2016
R. Memarbashi, A. Ghasemabadi: Fuzzy difference equations of volterra type, Int. J. Nonlinear Anal. Appl. 4, No.1, pp. 74‐78, 2013
J. Usenik, M. Vidiček, M. Vidiček, J. Usenik; Control of the logistics system using Laplace transforms and fuzzy logic, Logistics and sustainable transport, Vol. 1, issue 1, pp. 1‐19, 2008
J. Usenik, M. Repnik: System control in conditions of discrete stochastic input process, Journal of Energy Technology, Vol. 5, Iss. 1, pp. 37 ‐ 53, 2012
J. Usenik, T. Turnšek: Modeling Conflict Dynamics: System Dynamic Approach, Suistainable Logistics and Strategic Transportation Planning, IGI Global book series Advanced in Logistics, Operations, and management, Business Science Reference, Hershey PA, USA, pp. 273‐294, 2016
M. Bogataj, J. Usenik. Fuzzy approach to the spatial games in the total market, Int., j. prod. econ., Vol. 93‐94, pp. 493‐503, 2005
D. Kovačič, J. Usenik, M. Bogataj: Optimal decisions on investments in urban energy cogeneration plants ‐ extended MRP and fuzzy approach to the stochastic systems, International journal of production economics, 2016
J. Usenik, M. Bogataj: A fuzzy set approach for a location‐inventory model, Transp. plan. technol., Vol. 28, pp. 447‐464, 2005
J. Usenik: A fuzzy model of power supply system control, JET Journal of Energy technology, Vol. 5, Iss. 3, pp. 23–38, 2012
T.J. Ross: Fuzzy Logic with Engineering Applications, Second Edition, John Wiley & Sons Ltd., The Atrium, Southern Gate, Chichester, West Sussex, England, 2007
H. J. Zimmermann: Fuzzy Set Theory and its Applications, Fourth Edition, Kluwer Academic Publishers, Boston, pp. 352‐370, 2001
F. Cavallaro: A Takagi‐Sugeno Fuzzy Inference System for Developing a Sustainability Index of Biomass, Sustainability 7, pp. 12359‐12371, 2015
FuzzyTech 5.5: User`s Manual, INFORM GmbH, 2002
