High order robust fast finite time containment control for multi-agent systems

This paper studies the problem of robust containment with trivial sensitivity to both initial conditions and communication topology for multi-agent systems. In this way, based on the homogeneity property of the dynamic systems, a new nonlinear high order sliding surface for containment problem is proposed. This sliding surface has a fast finite time dynamics which causes remarkably reduction of containment sensitivity to the multi-agent initial conditions and communication topology. Accordingly, a high order fast finite time containment control (HOFFT-CC) protocol is established and the containment of multiple agents to a convex hull is realized. The proposed framework solves the fast containment problem for high order dynamics that are subjected to the external disturbance and furthermore, for both directed and undirected graph topology. Moreover, because of decoupling the agents’ dynamics and converting the multi-agent problem to some single agent problems, the structure of the proposed method is simpler and more straightforward in comparison with previous works. The finite time stability of the closed loop multi-agent systems based on the homogeneity theory and Lyapunov theorem, is analyzed and proved. The proof is produced throughout the negative degree homogeneity property of the closed loop dynamics along with asymptotical stability. In addition, simulation for a general third order multi-agent system in a two-dimensional space is accomplished and the results demonstrate the trivial sensitivity of containment to both initial conditions and communication topology.

Gel Formulation of Ethyl Acetate Garlic Extraction and Its Activity Against Staphylococcus Epidermis

Garlic is known to have antibacterial and antifungal activities. This research aims to formulate the gel materials extracted from the garlic and to investigate the antimicrobial activities to Staphylococcus epidermidis. The phytochemical screening showed that the gel materials of ethyl acetate consisted alkaloid, flavonoid, and saponin substances. The formulation of gel was synthesized with different variations of 1, 5, and 10%. In this research, the gel materials were analyzed to understand the stability, homogeneity, pH, viscosity and dispersive powers. The results showed that good abilities of gel based on the taste, aroma and consistency, while the homogeneity property of each samples is influenced by the presence of gel concentration. The viscosity property of gels accounted for 3201.02-1664.04 Cps with 2.95-3.8 cm of dispersive powers. The ability of antimicrobial showed that higher concentration of 5% and 10% gels showed greater inhibitory zones of 18,10 and 22,08 mm compared to 1% of concentration

Lie groupoids and algebroids applied to the study of uniformity and homogeneity of Cosserat media

A Lie groupoid, called second-order non-holonomic material Lie groupoid, is associated in a natural way to any Cosserat medium. This groupoid is used to give a new definition of homogeneity which does not depend on a material archetype. The corresponding Lie algebroid, called second-order non-holonomic material Lie algebroid, is used to characterize the homogeneity property of the material. We also relate these results with the previously obtained ones in terms of non-holonomic second-order [Formula: see text]-structures.

On possibility of utilization of side viewing radars for research of homogeneity of aerospace test plots

One of major properties of territories, designated for construction of aerospace test plots is homogeneity. In order to control the property of test plots homogeneity the statistic of Getis is widely used as its local indicator. If pixels on the object and its neighbors have similar high values the Getis statistics obtain a high value and vice versa a low one. In the article the process of reception the radars’ signal in the plane-parallel model of meteorological object is considered. The surface of the test plot may be taken as such a model. The condition of implementing a side viewing radar for obtaining the remote sensing data on rectangular grid for control of test plot on homogeneity using the Getis statistics is determined. It is shown that by selection of appropriate angle of slope the information from the test plot can be received by equal steps. In this case the homogeneity property of test plots are to be determined by help of Getis statistics on the basis of remote sensing data obtained on rectangular grid. The possibility for utilization of side viewing radars for obtaining the remote sensing data from rectangular grid at the test plot surface for further application of Getis statistics is researched.

Inverse problems of demand analysis and their applications to computation of positively-homogeneous Konüs–Divisia indices and forecasting

According to Pareto’s theory of consumer demand a rational representative consumer should choose their consumption bundle as the solution of a mathematical programming problem of maximization of the utility function under their budget constraint. The inverse problem of demand analysis is to recover the utility function from the demand functions. The answer to the question of solvability of this problem is based on the revealed preference theory. If the problem is unsolvable, one should apply regularization procedure by introducing irrationality indices. When recovering the utility function one puts a priori requirements on it. In this paper, we suggest including positively-homogeneity property into these requirements. We compare the setups with and without this requirement both theoretically and empirically and provide evidence in favor of requiring this property when computing economic indices for consumer representing consumption behavior of large number of various households for large time intervals.

On a numerical flux for the pedestrian flow equations

The pedestrian flow equations are formulated as the hyperbolic problem with a source term, completed by the eikonal equation yielding the desired direction of the pedestrian velocity. The operator splitting consisting of successive discretization of the eikonal equation, ordinary differential equation with the right hand side being the source term and the homogeneous hyperbolic system is proposed. The numerical flux of the Vijayasundaram type is proposed for the finite volume solution of the hyperbolic problem. The Vijayasundaram numerical flux, originally proposed for the hyperbolic problems possessing the homogeneity property is extended for pedestrian flow, where the homogeneity property is lost. The application of the proposed numerical flux is demonstrated on the physically relevant problem.