This paper focuses on an adaptive robust dynamic surface control (ARDSC) with composite adaptation laws (CAL) for a class of uncertain nonlinear systems in semi-strict feedback form. A simple and effective controller has been obtained by introducing dynamic surface control (DSC) technique and designing novel adaptation laws. First, the 'explosion of terms' problem caused by backstepping method in the traditional adaptive robust control (ARC) is avoided. Meanwhile, through a new proof philosophy the asymptotical output tracking that the ARC possesses is theoretically preserved. Second, when persistent excitation (PE) condition satisfies, true parameter estimates could be acquired via designing CALs which integrate the information of estimation errors. Finally, simulation results are presented to illustrate the effectiveness of the proposed method.

The orientation-preservation conditions and approximation errors of a dual-parametric bi-quadratic finite element method for the computation of both radially symmetric and general nonsymmetric cavity solutions in nonlinear elasticity are analyzed. The analytical results allow us to establish, based on an error equidistribution principle, an optimal meshing strategy for the method in cavitation computation. Numerical results are in good agreement with the analytical results. Introduction. Void formation on nonlinear elastic bodies under hydrostatic tension was observed and analyzed through a defect model by Gent and Lindley [8].Ball [2] established a perfect model and studied a class of bifurcation problems in nonlinear elasticity, in which voids form in an intact body so that the total stored energy of the material is minimized in a class of radially symmetric deformations. The work stimulated an intensive study on various aspects of radially symmetric cavitations (see, e.g., Sivaloganathan [19], Stuart [25], and a review paper by Horgan and Polignone [10], among many others).Müller and Spector [16] later developed a general existence theory in nonlinear elasticity that allows for cavitation, which is not necessarily radially symmetric, by adding a surface energy term. Sivaloganathan and Spector [21] deduced the existence of hole creating deformations without the need for the surface energy term under the assumption that the points (a finite number) at which the cavities can form are prescribed. Optimal locations where cavities can arise are also studied analytically [22,23] and numerically [14].Numerically computing cavities based on the perfect model of Ball is very challenging, due to the so-called Lavrentiev phenomenon [11]. Though there are numerical methods developed to overcome the Lavrentiev phenomenon in some nonlinear elasticity problems [1,3,12,17,18], they do not seem to be powerful enough for the cavitation problem. On the other hand, some numerical methods (see, e.g., [13,14,26]) have been successfully developed for cavitation computation on general domains with single or multiple prescribed defects, based on the defect model or the regularized perfect model [9,19,20]. In these models, one considers minimizing the total elastic energy of the form

Abstract. A numerical method using the truncation technique on the integrand is developed for computing singular minimizers or singular minimizing sequences in variational problems involving the Lavrentiev phenomenon. It is proved that the method can detect absolute minimizers with various singularities whether the Lavrentiev phenomenon is involved or not. It is also proved that, when the absolute infimum is not attainable, the method can produce minimizing sequences. Numerical results on the Manià's example and a 2-dimensional problem involving the Lavrentiev phenomenon with continuous Sobolev exponent dependence, are given to show the efficiency of the method.

Cross-dehydrogenative coupling (CDC), which enables the formation of carbon-carbon (C-C) and C-heteroatom bonds from the direct coupling of two C-H bonds or C-H/X-H bonds, represents a new state of the art in the field of organic chemistry. Iron, a prominent metal, has already shown its versatile application in chemical synthesis. This review attempts to provide a comprehensive understanding of the evolution of cross-dehydrogenative coupling via iron catalysis, as well as its application in synthetic chemistry.

A multiple-model adaptive robust dynamic surface control with estimator resetting is investigated for a class of semi-strict feedback nonlinear systems in this paper. The transient performance is mainly considered. The multiple models are composed of fixed models, one adaptive model, and one identification model that can be obtained when the persistent exciting condition is satisfied. The transient performance of the final tracking system can be improved significantly by designing proper switching mechanism during the parameter tuning procedure. The semi-globally uniformly ultimately bounded stability of the closed-loop system can be easily achieved because of the framework of adaptive robust dynamic surface control. Numerical examples are provided to demonstrate the effectiveness of the proposed multiple-model controller.Noting Equation (14), the nonlinear uncertainty d.x; t/ is unknown. The signal is generated by the following dynamic equation in implementation: P 0 D k.t/ 0 ; 0 .0/ D x.0/ ! 0 .0/ ! T .0/Â