RESUMEN
This paper studies the energy-constraint output formation control for swarm systems with leaderless and leader-following topology structures. Most existing results on output formation with the dynamic output feedback protocols focus on the swarm systems without the energy constraint, but it is well known that the energy constraint is critically important for practical applications. In order to analyze the impacts of the energy constraint, a new energy-constraint output formation protocol is proposed. First, by the observable decomposition approach, a dynamic output formation protocol is presented, which contains an energy-constraint term to restrict the whole consumption. Then, sufficient conditions for leaderless energy-constraint output formation are presented via establishing the relationship of the energy constraint and the matrix variables, where it is found that the designed gain matrices of the output formation protocol can ensure that the actual energy consumption is lower than the total energy supply. Especially, a partition checking algorithm is proposed to check those conditions, which can ensure the scalability and solvability of a swarm system. Moreover, the output formation center function is derived to depict the whole macroscopic movement of a swarm system. A nonsingular transformation approach is presented to unify leaderless energy-constraint output formation and energy-constraint output formation tracking into the same framework, which are usually discussed in different theoretical frameworks. Finally, two simulation examples are illustrated to show that the theoretical results about leaderless energy-constraint output formation and energy-constraint output formation tracking are correct.
RESUMEN
A two-year (2009-2011) field experiment was conducted to study the effects of different tillage modes, straw-returning, and their interactions on the soil total organic carbon (TOC) and labile organic carbon (LOC) components (easily oxidizable organic carbon (EOC), water-soluble organic carbon (WSOC), and microbial biomass carbon (MBC)) at the soil depths of 0-7, 7-14, and 14-21 cm in a farmland with rice-wheat double cropping. In all treatments of straw-returning, the TOC and LOC contents in each soil layer were significantly higher than those without straw-returning. Under plowing tillage, the MBC content in 0-7 cm soil layer was significantly higher than that under rotary tillage, but the EOC content was in adverse. Rotary tillage made the TOC content in 7 - 14 cm soil layer being significantly higher, as compared with plowing tillage. The TOC, WSOC, and MBC contents in 14-21 cm soil layer under plowing tillage were significantly higher than those under rotary tillage. Plowing tillage combined with rice and wheat straws-returning made the soil TOC content being higher than the other treatments.