Convergence analysis of estimated parameters for parametric nonlinear strict feedback system with unknown control direction

In this paper, the adaptive control and parameters identification problems are investigated for a class of linearly parametric strict feedback system with unknown control direction. Firstly, by using backstepping design procedure, the adaptive tracking control scheme combined with Nussbaum gain function is proposed. In the controller, the adaptive law of estimated parameters is derived from Lyapunov stability theorem and Nussbaum-type function. All the signals in closed-loop system are proved to be bounded. Secondly, the identification of unknown parameters in the strict feedback system with unknown control direction is studied. By constructing a novel Lyapunov function, a sufficient condition (PE condition), which can guarantee that the parameters estimation converge to the actual values of parameters, is obtained for the first time. Also, it is more simplified than the existing results on PE. Under the PE condition proposed here, it is shown that the parameters estimation errors are convergent to zero asymptotically by using Nussbaum function technique and Barbalat's lemma. Finally, illustrated examples are given to demonstrate the main results

Phenylboronic acid-diol crosslinked 6-<i>O</i>-vinylazeloyl-d-galactose nanocarriers for insulin delivery

A new block polymer named poly 3-acrylamidophenylboronic acid-b-6-O–vinylazeloyl-d-galactose (p(AAPBA-b-OVZG)) was prepared using 3-acrylamidophenylboronic acid (AAPBA) and 6-O-vinylazeloyl-D-galactose (OVZG) via a two-step procedure involving S-1-dodecyl-S-(α', α'-dimethyl-α″-acetic acid) trithiocarbonate (DDATC) as chain transfer agent, 2,2-azobisisobutyronitrile (AIBN) as initiator and dimethyl formamide (DMF) as solvent. The structures of the polymer were examined by Fourier transform infrared spectroscopy (FT-IR) and 1H NMR and the thermal stability was determined by thermal gravimetric analysis (TG/DTG). Transmission electron microscopy (TEM) and dynamic light scattering (DLS) were utilized to evaluate the morphology and properties of the p(AAPBA-b-OVZG) nanoparticles. The cell toxicity, animal toxicity and therapeutic efficacy were also investigated. The results indicate the p(AAPBA-b-OVZG) was successfully synthesized and had excellent thermal stability. Moreover, the p(AAPBA-b-OVZG) nanoparticles were submicron in size and glucose-sensitive in phosphate-buffered saline (PBS). In addition, insulin as a model drug had a high encapsulation efficiency and loading capacity and the release of insulin was increased at higher glucose levels. Furthermore, the nanoparticles showed a low-toxicity in cell and animal studies and they were effective at decreasing blood glucose levels of mice over 96 h. These p(AAPBA-b-OVZG) nanoparticles show promise for applications in diabetes treatment using insulin or other hypoglycemic proteins

On the characteristics of meromorphic functions with three weighted sharing values

AbstractIn this paper, we deal with the relation between the characteristic function of two nonconstant meromorphic functions with three weighted sharing values, which improves a result given by H.X. Yi and Y.H. Li. From this we establish a theorem which improves a result given by P. Li and C.C. Yang