Nonlinear surface waves propagating along composite waveguide consisting of nonlinear defocusing media separated by interfaces with nonlinear response

The nonlinear surface waves propagating along the ultra-thin-film layers with nonlinear properties separating three nonlinear media layers are considered. The model based on a stationary nonlinear Schrödinger equation with a nonlinear potential modeling the interaction of a wave with the interface in a short-range approximation is proposed. We concentrated on effects induced by the difference of characteristics of the layers and their two interfaces. The surface waves of three types exist in the system considered. The dispersion relations determining the dependence of surface waves energy on interface intensities and medium layer characteristics are obtained and analyzed. The localization energy is calculated in explicit form for many difference cases. The conditions of the wave localization on dependence of the layer and interface characteristics are derived. The surface waves with definite energies in specific cases existing only in the presence of the interface nonlinear response are found. All results are obtained in an explicit analytical form.

Quadrotor Stabilization and Tracking Using Nonlinear Surface Sliding Mode Control and Observer

We propose a control method wherein the estimated angles converge to the desired value for quadrotor attitude stabilization and position tracking. To improve the performance of a quadrotor system, the unmeasured states of the quadrotor are estimated using a sliding mode observer (SMO). We set up a quadrotor dynamic model and augment the quadrotor dynamics by an SMO. We also derive the control inputs by sliding mode control (SMC) and calculate the desired angle of the quadrotor to reach the target position with the control inputs. For fast convergence speed and increased robustness of tracking performance, a nonlinear sliding surface is applied to SMC. The angle of the quadrotor converges to the desired value through the operation of SMC with a nonlinear sliding surface. The target tracking performance is improved by adaptively switching the deceleration curve of the sliding mode surface with a nonlinear curve. Using a tracking system based on a nonlinear surface sliding mode control (NSMC) and SMO, the quadrotor reaches the target position with a decreased settling time. The performance and effectiveness of the proposed system are proved through simulation results.