Theory of differential inclusions and its application in mechanics

The following chapter deals with systems of differential equations with discontinuous right-hand sides. The key question is how to define the solutions of such systems. The most adequate approach is to treat discontinuous systems as systems with multivalued right-hand sides (differential inclusions). In this work three well-known definitions of solution of discontinuous system are considered. We will demonstrate the difference between these definitions and their application to different mechanical problems. Mathematical models of drilling systems with discontinuous friction torque characteristics are considered. Here, opposite to classical Coulomb symmetric friction law, the friction torque characteristic is asymmetrical. Problem of sudden load change is studied. Analytical methods of investigation of systems with such asymmetrical friction based on the use of Lyapunov functions are demonstrated. The Watt governor and Chua system are considered to show different aspects of computer modeling of discontinuous systems

Inhibition of the Nicotinic Acetylcholine Receptors by Cobra Venom α-Neurotoxins: Is There a Perspective in Lung Cancer Treatment?

Nicotine exerts its oncogenic effects through the binding to nicotinic acetylcholine receptors (nAChRs) and the activation of downstream pathways that block apoptosis and promote neo-angiogenesis. The nAChRs of the α7 subtype are present on a wide variety of cancer cells and their inhibition by cobra venom neurotoxins has been proposed in several articles and reviews as a potential innovative lung cancer therapy. However, since part of the published results was recently retracted, we believe that the antitumoral activity of cobra venom neurotoxins needs to be independently re-evaluated

The regularized visible fold revisited

The planar visible fold is a simple singularity in piecewise smooth systems. In this paper, we consider singularly perturbed systems that limit to this piecewise smooth bifurcation as the singular perturbation parameter $\epsilon\rightarrow 0$. Alternatively, these singularly perturbed systems can be thought of as regularizations of their piecewise counterparts. The main contribution of the paper is to demonstrate the use of consecutive blowup transformations in this setting, allowing us to obtain detailed information about a transition map near the fold under very general assumptions. We apply this information to prove, for the first time, the existence of a locally unique saddle-node bifurcation in the case where a limit cycle, in the singular limit $\epsilon\rightarrow 0$, grazes the discontinuity set. We apply this result to a mass-spring system on a moving belt described by a Stribeck-type friction law

High-order sliding mode control of a DC motor drive via a switched controlled multi-cellular converter

In this article, we present a high-order sliding mode controller of a DC motor drive connected to a multi-cellular converter. More specifically, we design a second-order (super-twisting) control algorithm for the speed regulation of a DC motor. For this, a switching control for the multi-cellular converter is derived in order to supply the correct reference value for the speed regulation. A practical implementation of the controller is realised using a laboratory set-up. The performance and the validity of the controller are shown experimentally