Exponential super-twisting control for nonlinear systems with unknown polynomial perturbations.

The study focuses on the control of nonlinear dynamic systems in the presence of parameter uncertainties, unmodeled dynamics, and external disturbances. The lumped perturbation is assumed to be bounded within a polynomial in the system state with the polynomial parameters and degrees unknown a priori such that it accommodates a quite wider range dynamic systems. Based on the studies in recent super-twisting algorithm designs and the idea from adaptive sliding mode control for nonlinear systems with uncertainties, we propose a novel adaptive super-twisting algorithm with exponential reaching law, or exponential super-twisting algorithm (ESTA), for the high-stability and acceptable accuracy control of the aimed nonlinear dynamics. The stability analysis and practical finite-time (PFT) convergence are proven using Lyapunov theory and an intuitive analysis of the control behaviour. Simulations are performed to compare the proposed ESTA with the existing super-twisting method and the traditional proportional integral differential control. The simulation results demonstrate the effectiveness of the proposed ESTA in terms of the fastest settling time and the smallest overshoot.

Cinnamic acid regulates the intestinal microbiome and short-chain fatty acids to treat slow transit constipation.

BACKGROUND: Slow transit constipation (STC) is a disorder with delayed colonic transit. Cinnamic acid (CA) is an organic acid in natural plants, such as Radix Scrophulariae (Xuan Shen), with low toxicity and biological activities to modulate the intestinal microbiome. AIM: To explore the potential effects of CA on the intestinal microbiome and the primary endogenous metabolites-short-chain fatty acids (SCFAs) and evaluate the therapeutic effects of CA in STC. METHODS: Loperamide was applied to induce STC in mice. The treatment effects of CA on STC mice were assessed from the 24 h defecations, fecal moisture and intestinal transit rate. The enteric neurotransmitters: 5-hydroxytryptamine (5-HT) and vasoactive intestinal peptide (VIP) were determined by the enzyme-linked immunosorbent assay. Hematoxylin-eosin and Alcian blue and Periodic acid Schiff staining were used to evaluate intestinal mucosa's histopathological performance and secretory function. 16S rDNA was employed to analyze the composition and abundance of the intestinal microbiome. The SCFAs in stool samples were quantitatively detected by gas chromatography-mass spectrometry. RESULTS: CA ameliorated the symptoms of STC and treated STC effectively. CA ameliorated the infiltration of neutrophils and lymphocytes, increased the number of goblet cells and acidic mucus secretion of the mucosa. In addition, CA significantly increased the concentration of 5-HT and reduced VIP. CA significantly improved the diversity and abundance of the beneficial microbiome. Furthermore, the production of SCFAs [including acetic acid (AA), butyric acid (BA), propionic acid (PA) and valeric acid (VA)] was significantly promoted by CA. The changed abundance of Firmicutes, Akkermansia, Lachnoclostridium, Monoglobus, UCG.005, Paenalcaligenes, Psychrobacter and Acinetobacter were involved in the production of AA, BA, PA and VA. CONCLUSION: CA could treat STC effectively by ameliorating the composition and abundance of the intestinal microbiome to regulate the production of SCFAs.