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Beam splitters, especially those with tunable split ratios, play significant role in interferometers, spectrometers, and communication systems. To this end, we proposed a polarization-controllable beam splitter based on dielectric metasurface composed of an array of dielectric pillars. The dielectric metasurface presents phase gradients along two orthogonal directions, say, x- and y- axis, with each phase gradient applicable to one of two orthogonal linear polarizations. Due to the orthogonality of the dual phase gradients in both position and polarization, an elliptically polarized incident beam can be diffracted into two refracted beams, one lies within xoz plane and the other in yoz plane. More importantly, the split ratio of the two refracted beams is continuously tunable by changing the ellipticity of incident beam. Under extreme case, x- or y- polarized incident beam is refracted into one beam, but in different planes for different kind of linear polarization. Besides, the refracted angle of each refracted beam in respective refracted plane can be easily set by adjusting the phase difference of adjacent rows or columns of metasurface. With same method, a polarization-controllable dual-wavelength beam splitter is also achieved on the basis of phase-gradient metasurface. Such a noncoplanar beam splitter with tunable split ratios may play significant role in novel miniature optical devices and systems.

This paper concerns the design and optimisation of two-dimensional (2D) repetitive control of nonlinear systems based on the Takagi-Sugeno (T-S) fuzzy model. First, a continuous-discrete 2D model of nonlinear repetitive-control systems based on T-S fuzzy model is constructed by utilizing the 2D characteristics of continuous control and discrete learning actions in the repetitive-control process. Next, a fuzzy Lyapunov-Krasovskii functional derives the linear-matrix-inequality-based stability condition with a low conservatism. Two positive and two nonzero parameters in the fuzzy Lyapunov-Krasovskii functional tune the control and learning actions. Then the particle swarm optimisation algorithm based on a 2D performance index searches for the best parameter combination, resulting in the optimal 2D controller gains. A numerical example is given to demonstrate the effectiveness of the method.

In this paper, the issue of disturbance rejection of nonlinear repetitive control system (RCS) based on a continuous-discrete two-dimensional (2D) model is studied. Since a RCS involves continuous control and discrete learning, higher tracking performance may be realizable by taking into account these two different actions in system design. This paper construct a fuzzy RCS based on T-S model at first. Then, an improved fuzzy-equivalent-input-disturbance (IFEID)-based 2D RCS is presented to achieve both high tracking precision of periodic input and satisfactory rejection of aperiodic disturbances. Stability conditions of two subsystems are derived by exploiting separation theorem to ease the solution of state-feedback and observer gains. A design algorithm is presented via the concept of parallel distributed compensation. A simulation and a comparison demonstrate the availability and advantage of the IFEID-based 2D RCS approach.

This paper concerns robust stabilization for a class of nonlinear systems with uncertainties and disturbaces. The equivalent-input-disturbance (EID) approach is utilized to estimate the influence of nonlinearities and exogenous disturbances on the output of the system. A robust stability condition is derived in terms of linear matrix inequalities. Moreover, two parameters are used to tune the robustness of the system. Simulation results show that it is more effective to stabilize the system using the developed method than using the sliding-mode control (SMC) method.

Aiming at the problems of slow recognition, low efficiency and degree of automation in handwritten letter recognition system at present, a handwritten letter recognition system based on extreme learning machine is designed in this paper. The system is implemented by mixed programming with MATLAB and visual studio, it can reads, normalize, binarize and extract the handwritten letter images. The real-time interactive recognition of handwritten letters can be realized on the basis of training the simple pictures by using the identification model of the extreme learning machine algorithm. The experimental results show that the handwriting recognition system based on extreme learning machine designed in this paper can recognize 98.82% of handwritten letters and greatly reduce learning and testing time. Compared with BP neural network and other recognition algorithms, its training times have been reduced by hundreds or even thousands of times. At the same time, there is no manual intervention in the entire learning and testing process, which improves the automation of handwriting recognition.