Curvas elípticas en criptografía y su aplicación en bitcoin

*La criptografía estudia las formas en que se puede transformar un texto legible a uno ilegible y viceversa. Entre las técnicas más utilizadas se encuentran DSA, RSA, AES y Diffie-Hellman, donde la mayoría de estos métodos tienen una implementación con curvas elípticas. ● Una curva elíptica es de la forma y2=x3+Ax+B, y posee sus propia definición para la suma de dos puntos y multiplicación (suma continua de puntos)

Sinteza sustava upravljanja s proporcionalno-derivacijskim regulatorom zasnovana na neizrazitim diferencijalnim jednadžbama

This paper reports a fuzzy differential equations approach for the modeling of initial condition uncertainty for a proportional derivative closed-loop control of a direct current motor. Uncertainties are considered on the precision of the sensing devices installed on a driver. The closed-loop system is designed for a plant modeled with fuzzy differential equations. Satisfactory analytic and numerical results for the position regulation problem for ideal case and also considering perturbed initial conditions are reported.U radu je razvijen postupak sinteze proporcionalno-derivacijskog regulatora za upravljanje istosmjernim motorom s neizrazitim (engl. fuzzy) početnim uvjetima zasnovane na neizrazitim diferencijalnim jednadžbama. Pritom je uzeta u obzir nesigurnost određena mjernom preciznošću senzora. U predloženom postupku se zatvoreni regulacijski krug dizajnira korištenjem neizrazitih diferencijalnih jednadžbi. Primjenom projektiranog regulatora na probleme pozicioniranja u idealnom slučaju te u slučaju koji uzima u obzir perturbirane početne uvjete ostvareni su zadovoljavajući analitički i numerički rezultati

Design of a fuzzy controller via fuzzy Lyapunov synthesis for the stabilization of an inertial wheel pendulum

[ES] En el presente trabajo se reporta el diseño de un controlador difuso tipo Mamdani para el problema de estabilización de un péndulo de rueda inercial. Las reglas difusas son obtenidas mediante la síntesis difusa de Lyapunov, lo cual permite mantener al mínimo el uso de la heurística, y desde la etapa de diseño garantizar estabilidad en lazo cerrado. Por otra parte el diseño de las reglas difusas es mucho más simple que la ardua tarea de resolver las ecuaciones diferenciales no lineales usadas tradicionalmente para modelar sistemas de control. Merece énfasis especial el hecho de que el diseño se hace libre del modelo matemático del sistema a controlar.[EN] In this paper was presented the design of a Mamdani type fuzzy controller to solve the stabilization problem for an inertial wheel pendulum. The fuzzy rule base are designed following the fuzzy Lyapunov synthesis, which guarantee the local asymptotic stability of the closed-loop system, by using a Lyapunov function whose time-derivative is negative semidefinite, while the use of heuristics is minimized in the design process. Moreover, the design of the fuzzy rule base is simplest than the hard task of solve the nonlinear differential equations traditionally used to model control systems. Deserves special emphasis the fact that the design is made without a mathematical model of the inertia wheel pendulum.Parcialmente financiando por el Tecnológico Nacional de Mexico con los proyectos 5862.16-P, ´ 5867.16-P, PRODEP ITTIJ-CA-8 y CONACYT 268364.Cazarez-Castro, NR.; Aguilar, LT.; Cardenas-Maciel, SL.; Goribar-Jiménez, CA.; Odreman-Vera, M. (2017). Diseño de un Controlador Difuso mediante la Síntesis Difusa de Lyapunov para la Estabilización de un Péndulo de Rueda Inercial. 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Prentice Hall, EEUU.Korotnikov, V., 1998. Partial Stability and Control, 1st Edition. SpringerBirkhäuser Basel, EEUU.Lyapunov, A., 1892. The general problem of the stability of motion (in russian). Phd, Univ. Kharkov.Mamdani, E., Assilian, S., 1975. An experiment in linguistic synthesis with a fuzzy logic controller. International Journal of Man-Machine Studies 7 (1), 1-13.Margaliot, M., Langholz, G., 1999. Fuzzy lyapunov-based approach to the design of fuzzy controllers. Fuzzy Sets and Systems 106 (1), 49-59.Martinez-Soto, R., Rodriguez, A., Castillo, O., Aguilar, L. T., 2012. Gain optimization for inertia wheel pendulum stabilization using particle swarm optimization and genetic algorithms. International Journal of Innovative Computing, Information and Control 8 (6), 4421-4430.Ng, W. M., Chang, D. E., Song, S.-H., 2013. Four representative applications of the energy shaping method for controlled lagrangian systems. Journal of Electrical Engineering and Technology 8 (6), 1579-1589.Qaiser, N., Iqbal, N., Hussain, A., Qaiser, N., 2006. Stabilization of non-linear inertia wheel pendulum system using a new dynamic surface control based technique. In: Engineering of Intelligent Systems, 2006 IEEE International Conference on. pp. 1-6.Qaiser, N., Iqbal, N., Hussain, A., Qaiser, N., 2007. Exponential stabilization of the inertia wheel pendulum using dynamic surface control. Journal of Circuits, Systems and Computers 16 (01), 81-92.Ye, H., Wang, H., Wang, H., Nov 2007. Stabilization of a pvtol aircraft and an inertia wheel pendulum using saturation technique. IEEE Transactions on Control Systems Technology 15 (6), 1143-1150.Yi, J., Yubazaki, N., 2000. Stabilization fuzzy control of inverted pendulum systems. Artificial Intelligence in Engineering 14 (2), 153 - 163