In this paper, a new hybrid unscented Kalman (UKF) and unscented H ∞ (U H ∞ F) filter is presented that can adaptively adjust its performance better than that of either UKF and/or U H ∞ F , accordingly. In this way, two Takagi-Sugeno-Kang (TSK) fuzzy logic systems are presented to adjust automatically some weights that combine those UK and U H ∞ filters, independent of the dynamics of the problem. Such adaptive fuzzy hybrid unscented Kalman/ H ∞ filter (AFUK H ∞ ) is based on the combination of gain, a priori state estimation, and a priori measurement estimation. The simulation results of an inverted pendulum and a re-entry vehicle tracking problem clearly demonstrate robust and better performance of this new AFUK H ∞ filter in comparison with those of both UKF and U H ∞ F, appropriately. It is shown that, therefore, the new presented AFUK H ∞ filter can simply eliminate the need for either UKF or U H ∞ F effectively in the presence of Gaussian and/or non-Gaussian noises.

SUMMARYThis paper presents a novel robust hybrid fractional order proportional derivative sliding mode controller (HFOPDSMC) for 2-degree of freedom (2-DOF) robot manipulator based on extended grey wolf optimizer (EGWO). Sliding mode controller (SMC) is remarkably robust against the uncertainties and external disturbances and shows the valuable properties of accuracy. In this paper, a new fractional order sliding surface (FOSS) is defined. Integrating the fractional order proportional derivative controller (FOPDC) and a new sliding mode controller (FOSMC), a novel robust controller based on HFOPDSMC is proposed. The bounded model uncertainties are considered in the dynamics of the robot, and then the robustness of the controller is verified. The Lyapunov theory is utilized in order to show the stability of the proposed controller. In this paper, the EGWO is developed by adding the emphasis coefficients to the typical grey wolf optimizer (GWO). The GWO and EGWO, then, are applied to optimize the proposed control parameters which result in the optimized GWO-HFOPDSMC and EGWO-HFOPDSMC, respectively. The effectivenesses of the optimized controllers (GWO-HFOPDSMC and EGWO-HFOPDSMC) are completely verified by comparing the simulation results of the optimized controllers with the typical FOSMC and HFOPDSMC.

The global stability analysis for the mathematical model of an infectious disease is discussed here. The endemic equilibrium is shown to be globally stable by using a modification of the Volterra–Lyapunov matrix method. The basis of the method is the combination of Lyapunov functions and the Volterra–Lyapunov matrices. By reducing the dimensions of the matrices and under some conditions, we can easily show the global stability of the endemic equilibrium. To prove the stability based on Volterra–Lyapunov matrices, we use matrices with the symmetry properties (symmetric positive definite). The results developed in this paper can be applied in more complex systems with nonlinear incidence rates. Numerical simulations are presented to illustrate the analytical results.

During the past decades, there have been a great amount of research activities in approximate problem solving to estimate the real amount of states of dynamical systems using measurement data corrupted with noise. One of the most famous approximate solving methods is Unscented Kalman Filter (UKF). In UKF, the estimation is based on a collection of symmetrical sigma points around an a priori-estimated state. In this paper, Genetic Algorithm (GA) is firstly used to optimally select the best coefficients of the symmetrical sigma points related to Scaled Unscented Transform in UKF (GA-UKF) to minimize the mean of squared error of estimations. Moreover, GA is also used to select a collection of asymmetrical sigma points (GA-ASKF) to minimize the mean of squared error of estimations together with same statistics of the mean and covariance matrix. The new idea of the asymmetric sigma points Kalman filter of this paper which are optimally found again by using GA evidently outperforms both conventional UKF and GA-UKF of this paper in estimating the states of dynamical systems.

State estimation and dynamical model identification from the observed data have attracted much research effort during recent years. In this paper, an identification method of a system based on the unscented Kalman filter (UKF) and group method of data handing (GMDH)-type neural network is introduced and applied. Probabilistic metrics, instead of deterministic metrics, are used to obtain a robust Pareto multi-objective optimum design of the UKF-based GMDH-type neural network. The simulation results show that the UKF-based training algorithm performs well in modelling some explosive cutting and forming processes, and exhibited more robustness in comparison with those using a traditional GMDH-type neural network.