FeCl₃‑Promoted [3 + 2] Annulations of γ‑Butyrolactone Fused Cyclopropanes with Heterocumulenes

The [3 + 2] annulations of γ-butyrolactone fused donor–acceptor (D–A) cyclopropanes with aromatic isothiocyanates and dialkyl carbodiimides promoted by FeCl₃ is reported. A series of bicyclic/polycyclic γ-butyrolactone fused thioimidates and γ-butyrolactone fused amidines containing four contiguous stereogenic centers were obtained in excellent yields as single stereoisomers

Lewis Acid-Catalyzed Annulations of Geminally Disubstituted Cyclopropanes with Aldehydes or 1,3,5-Triazinanes

Under the catalysis of simple Lewis acid catalysts, 2-(1-aroylcyclopropyl)malonates demonstrated unique reactivities in annulation reactions with aryl/alkyl aldehydes, paraformaldehyde, and 1,3,5-triazinanes. Three types of structurally diverse cyclic products that are otherwise not easy to obtain were generated in moderate to good yields and excellent diastereoselectivities. Possible reaction pathways leading to these products were proposed on the basis of the results of control experiments

Fast smooth second-order sliding mode control for systems with additive colored noises

<div><p>In this paper, a fast smooth second-order sliding mode control is presented for a class of stochastic systems with enumerable Ornstein-Uhlenbeck colored noises. The finite-time mean-square practical stability and finite-time mean-square practical reachability are first introduced. Instead of treating the noise as bounded disturbance, the stochastic control techniques are incorporated into the design of the controller. The finite-time convergence of the prescribed sliding variable dynamics system is proved by using stochastic Lyapunov-like techniques. Then the proposed sliding mode controller is applied to a second-order nonlinear stochastic system. Simulation results are presented comparing with smooth second-order sliding mode control to validate the analysis.</p></div

The control signal of SFS-SOSM control.

<p>The control signal of SFS-SOSM control.</p

The phase plot of SFS-SOSM control.

<p>The phase plot of SFS-SOSM control.</p

The phase plot of SSOSM control.

<p>The phase plot of SSOSM control.</p

<i>s</i> of SSOSM control.

<p><i>s</i> of SSOSM control.</p

The tracking error of SSOSM control.

<p>The tracking error of SSOSM control.</p

of SSOSM control.

<p> of SSOSM control.</p

The block diagram of SFS-SOSM control design.

<p>The block diagram of SFS-SOSM control design.</p