One of the nonlinear optical phenomena which arise out of a (3) ,nonlinearity, is the intensity dependence of the refractive index. In this paper, we describe this phenomenon based on the nonlinear coherent states approach. We show that the deformed two-dimensional oscillator algebra can be used to describe this nonlinear optical system. Then, we construct the nonlinear coherent states for this nonlinear optical system and study their quantum statistical properties. Finally, we find that by changing nonlinearity of the media, it is possible to control the nonclassical properties of the system.

Quantum state teleportation plays a significant role in the field of quantum information transfer. In this article, we proposed the teleportation of a state prepared as a superposition of a coherent state and a vacuum state, using a generalized hybrid entangled state. By considering a setup that includes a beam splitter and a photon detector, and under appropriate conditions, successful teleportation of the entangled state composed of the coherent state and the vacuum state can be achieved.Furthermore, it has been shown that when considering entangled states of even or odd coherent states and the vacuum state, the success probability significantly increases to 0.5. These results indicate that the generalized hybrid entangled state plays a crucial role in the quantum teleportation of these states.

The coupled coherent states method (CCS) has been optimized in order to remove the two complexities in the simulation of the ground state of electronic systems. These two complexities are the necessity of the energy restriction in the process of generating CS grid, and the essential refinement of the grid in each time-step. The optimized method which for the first time has been applied for simulation of the potential well of the ground state of one-electron systems such as 2H . The simulation results on the basis of a grid containing only 500 coherent states show a very good consistency with the exact curve. Implementing grids with more coherent states into the simulation would lead to a better consistency with the exact values.

In this research, we study the coherent states of a deformed nonlinear harmonic oscillator. We use the perturbation theory to compute eigenstates and eigen-values ​​for a deformed nonlinear harmonic oscillator and then define the generalized coherent states based on the Gazeau-Klauder formulation. Then, using the Mandel parameter and the second-order correlation function, we will investigate the statistical properties of the system. The analysis shows that the coherent states for a deformed and non-deformed nonlinear harmonic oscillator follows the sub-Poissonian and super-Poissonian statistics, and exhibits the antibunching and bunching effects, respectively. In addition, we show that the anti-correlation function for a deformed nonlinear oscillator is strongly fluctuating and irregular. Also, the anti-correlation function of a non-deformed nonlinear harmonic oscillator shows the phenomena of collapse and revival of fractional revelations. We also examine the limits of different parameters so that the obtained results are valid.

In this paper, a novel filter is provided that estimates the states of any nonlinear system, both in the presence and absence of uncertainty with high accuracy. It is well understood that a robust filter design is a compromise between the robustness and the estimation accuracy. In fact, a robust filter is designed to obtain an accurate and suitable performance in presence of modelling errors. So in the absence of any unknown or time-varying uncertainties, the robust filter does not provide the desired performance. The new method provided in this paper, which is named hybrid robust cubature Kalman filter (CKF), is constructed by combining a traditional CKF and a novel robust CKF. The novel robust CKF is designed by merging a traditional CKF with an uncertainty estimator so that it can provide the desired performance in the presence of uncertainty. Since the presence of uncertainty results in a large innovation value, the hybrid robust CKF adapts itself according to the value of the normalized innovation. The CKF and robust CKF filters are run in parallel and at any time, a suitable decision is taken to choose the estimated state of either the CKF or the robust CKF as the final state estimation. To validate the performance of the proposed filters, two examples are given that demonstrate their promising performance.

Singular systems behave more powerfully in terms of dynamical system modeling than ordinary state space systems. Since the algebraic equations in singular models can describe the systems constraints, nonlinear singular systems can present a general method for modeling and controlling constrained dynamical systems. This paper discusses an adaptive control for nonlinear singular systems which satisfy Lipschitz condition. Adaptive methods for singular systems are hardly ever investigated in literatures; however they are very useful methods in practice because the adaptive mechanism during the adaptive control can adjust the controller for a system with the unknown structures and parameters to improve the system performance. The presented controller is composed of a state feedback approach with adaptive gains and a mechanism to adjust the gains based on the Lyapunov stability theorem. First the controller is designed to stabilize the system, as a result, it is extended for the tracking problem. A simulation on a mobile robot singular model is provided to illustrate the effectiveness of the proposed control approach.

In the several past years, Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) have became basic algorithm for state-variables and parameters estimation of discrete nonlinear systems. The UKF has consistently outperformed for estimation. Sometimes least estimation error doesn't yield with UKF for the most nonlinear systems. In this paper, we use a new approach for a two variable state nonlinear systems which it is called Rotated UKF (R_UKF). R_UKF can be reduced estimation error and reached for least error in state estimation.