Mixed H₂/H∞ Tracking Control with Constraints for Single Quadcopter Carrying a Cable-suspended Payload

In order to control a single quadcopter with a cable-suspended payload to follow the desired trajectory, a mixed H₂/H∞ controller with constraints is developed. Firstly, the Euler-Lagrange dynamic model is built and linearized. Then the extended model for path tracking problem is designed. Based on linear matrix inequality (LMI), state feedback controller H₂ and H∞ with constraints is illustrated. Aiming to maintain a good balance in transient behaviors and frequency-domain performance, the mixed controller is presented. Finally, the control strategies are utilized in a simulation test and the result validates the proposed method

The Fate of the Accelerating Universe

The presently accelerating universe may keep accelerating forever, eventually run into the event horizon problem, and thus be in conflict with the superstring idea. In the other way around, the current accelerating phase as well as the fate of the universe may be swayed by a negative cosmological constant, which dictates a big crunch. Based on the current observational data, in this paper we investigate how large the magnitude of a negative cosmological constant is allowed to be. In addition, for distinguishing the sign of the cosmological constant via observations, we point out that a measure of the evolution of the dark energy equation of state may be a good discriminator. Hopefully future observations will provide much more detailed information about dark energy and thereby indicates the sign of the cosmological constant as well as the fate of the presently accelerating universe.Comment: 16 pages, 5 figures, LaTe