A simple one-pot hydrothermal synthesis route has been employed to fabricate the bismuth-doped (Bi-doped) anatase TiO 2 hollow thin sheets with {001} facets exposed. Controlling BiVO 4 precursor concentration plays a key role in tuning the morphology and the Bi doping concentration of TiO 2 hollow thin sheet catalysts. The photocatalytic activity of as-prepared catalysts was evaluated through the photodegradation of different organic dyes under visible light irradiation (>400 nm), including methylene blue (MB), methyl orange (MO), rhodamine-B (RhB), and p-nitroaniline (PNA). Results showed that the optimal dopant of 0.8 atom % Bi in TiO 2 achieved the best photocatalytic activity, especially for possessing a much higher photodegradation of PNA, which could be ascribed to the results of photoinduced charge separation and transfer combined with low bulk recombination of charge carriers. This discussion demonstrates that the design of new TiO 2 nanostructures for application in solar energy conversion could be easily achieved by coupling Bi cation-doping and active facets with hollow thin sheet morphology.

This article investigates the robust output regulation problem for unknown nonlinear strict-feedback systems with input delay. Nonlinear fuzzy internal model and adaptive fuzzy backstepping control are integrated to obtain a feedforward-feedback composite controller. As a distinctive feature, Pade approximation technique is introduced to deal with the input delay of nonlinear output regulation problem for the first time. The process of control strategy can be divided into two steps. In the first step, a novel nonlinear fuzzy internal model is designed to get the feedforward compensator. In the second step, an adaptive fuzzy backstepping control scheme is proposed to get the feedback controller, which can guarantee semiglobally uniformly ultimately bounded of the closed-loop system. Simulation results of an interconnected power system show the validity of the theoretical results.

This article investigates the robust optimal output regulation problem for the constrained uncertain nonlinear systems. A two‐step design framework is proposed to overcome the difficulties brought by uncertainties, constraint and performance optimization. First, the feedforward controller is designed by the internal model principle, and the robust output regulation problem is transformed into the robust stabilization problem. Then, the optimal control problem with input saturation is further considered in the robust feedback controller design process. With the help of a non‐quadratic cost functional, actor‐critic algorithm and robust redesign technique are brought together to design the constrained robust optimal feedback controller. Finally, stability analysis based on Lyapunov method shows that all the signals of the closed‐loop system remain bounded, and the tracking error is uniformly ultimately bounded with arbitrarily small ultimate bound. Simulation results illustrate the effectiveness of the proposed methodology.

We propose a new estimation procedure for estimating the unknown parameters and function in partial functional linear regression. The asymptotic distribution of the estimator of the vector of slope parameters is derived, and the global convergence rate of the estimator of unknown slope function is established under suitable norm. The convergence rate of the mean squared prediction error for the proposed estimators is also established. Based on the proposed estimation procedure, we further construct the penalized regression estimators and establish their variable selection consistency and oracle properties. Finite sample properties of our procedures are studied through Monte Carlo simulations. A real data example about the real estate data is used to illustrate our proposed methodology.

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