On the Lagrangian Structure of Reduced Dynamics Under Virtual Holonomic Constraints

This paper investigates a class of Lagrangian control systems with $n$ degrees-of-freedom (DOF) and n-1 actuators, assuming that $n-1$ virtual holonomic constraints have been enforced via feedback, and a basic regularity condition holds. The reduced dynamics of such systems are described by a second-order unforced differential equation. We present necessary and sufficient conditions under which the reduced dynamics are those of a mechanical system with one DOF and, more generally, under which they have a Lagrangian structure. In both cases, we show that typical solutions satisfying the virtual constraints lie in a restricted class which we completely characterize.Comment: 23 pages, 5 figures, published online in ESAIM:COCV on April 28th, 201

The prevalence of severe depression in Iranian older adult:a meta-analysis and meta-regression

Background: Depression is one of the most common psychiatric disorders in the older adult and one of the most common risk factors for suicide in the older adult. Studies show different and inconsistent prevalence rates in Iran. This study aims to determine the prevalence of severe depression in Iranian older adult through a meta-analysis approach. Methods: The present meta-analysis was conducted between January 2000-August 2019. Articles related to the subject matter were obtained by searching Scopus, Sciencedirect, SID, magiran, Barakat Knowledge Network System, Medline (PubMed), and Google Scholar databases. The heterogeneity of the studies was evaluated using I 2 index and the data were analyzed in Comprehensive Meta-Analysis software. Results: In a study of 3948 individuals aged 50-90 years, the overall prevalence of severe depression in Iranian older adult was 8.2% (95% CI, 4.14-6.3%) based on meta-analysis. Also, in order to investigate the effects of potential factors (sample size and year of study) on the heterogeneity of severe depression in Iranian older adult, meta-regression was used. It was reported that the prevalence of severe depression in Iranian older adult decreased with increasing sample size and increasing years of the study, which is significantly different (P &lt; 0.05). Conclusion: Considering the high prevalence of severe depression in Iranian older adult, it is necessary for health policy makers to take effective control measures and periodic care for the older adult. </p