چكيده به لاتين
In this thesis, the issue of incorporation of the fractional Kalman filter and non-standard finite difference discretization method and also, synchronization of fractional chaotic systems using sliding mode control will be discussed. This important because the fractional stochastic systems are still in the early stages of research. This thesis consists of two main parts.
In the first part, the non-standard finite difference discretization method is studied and its applications in the discretization of deterministic systems and stochastic systems are investigated. Then, this method for the first time is developed for stochastic systems. Due to the importance of estimating of the fractional stochastic systems and its practical application, the discretization method is merged with fractional Kalman filter. Then, using the fractional Kalman filter the states of linear stochastic systems are estimated. In order to estimate the state of nonlinear systems, this method is extended to nonlinear systems and using fractional extended Kalman filter the states of fractional chaotic systems are estimated.
In the second part of this thesis, the issue of synchronization of fractional chaotic systems is discussed. For this purpose, an adaptive-fuzzy sliding mode controller is proposed. The chaotic master and slave systems are intended as unknown systems. For this purpose, the chaotic systems are approximated using the adaptive neural fuzzy inference system. Then, using the proposed controller, the slave system is synchronized with master system.
