Leader-following scaled consensus of second-order multi-agent systems under directed topologies

ABSTRACT

This paper investigates the leader-following scaled consensus problem of second-order multi-agent systems under directed topologies. Three novel leader-following scaled consensus protocols are designed. First, a novel scaled consensus protocol is proposed. It can guarantee the velocity of each agent in one sub-group exactly follow that of a leader, and the follower agents achieve scaled consensus. Second, another proposed protocol enables the agents' positions and velocities of one sub-group accurately track those of a leader, and the follower agents achieve scaled consensus. Third, consider the case where the leader's states available to one or multiple followers and the leader travels with a varying velocity, a novel scaled consensus tracking protocol is proposed. Sufficient and necessary conditions are obtained to guarantee scaled consensus tracking for the three cases,respectively. Finally, simulation examples are made to verify the effectiveness of the theoretical results.     

Extraction and separation of acetanilide herbicides in beans based on metal-organic framework MIL-101 (Zn) as sorbent

ABSTRACT

An extraction method based on metal-organic framework has been developed and applied to acetanilide herbicides, including metazachlor, propanil, pretilachlor, and butachlor, in black beans, red beans, and kidney beans. The acetanilide herbicides are extracted with a mixture of ethyl acetate and n-hexane. The extract solution is absorbed and purified with metal-organic framework MIL-101 (Zn). The separation and determination of four acetanilide herbicides were implemented by high-performance liquid chromatography. The experimental parameters were evaluated by a univariate method and orthogonal experiments. The presented method can obtain effective extraction and purification. The detection limits for metazachlor, propanil, pretilachlor, and butachlor were 0.58, 0.90, 1.78 and 1.18 µg/kg, respectively. The average recoveries of the acetanilide herbicides at spiked concentrations of 10, 50, and 100 µg/kg ranged from 86.9% to 119.0%, and relative standard deviations were equal to or lower than 2.80%.