A dynamic mathematical model of fish algae consumption with an impulsive control strategy is proposed and analyzed in detail. It is shown that the system has a globally asymptotically stable algae-eradication periodic solution which can be obtained using the Floquet theory of impulsive differential equations and small-amplitude perturbation techniques. The conditions for the permanence of the system can also be determined. Numerical results for impulsive perturbations show the rich dynamic behavior of the system. All these results may be useful in controlling eutrophication.
This paper investigates a dynamic mathematical model of fish algae consumption with an impulsive control strategy analytically. It is proved that the system has a globally asymptotically stable algae-eradication periodic solution and is permanent by using the theory of impulsive equations and small-amplitude perturbation techniques. Numerical results for impulsive perturbations demonstrate the rich dynamic behavior of the system. Further, we have also compared biological control with chemical control. All these results may be useful in controlling eutrophication.
This paper presents an efficient entry guidance law for no-fly zone avoidance, which is based on the recently developed linear pseudospectral model predictive control. First, a simple mapping relation of the position of the no-fly zone between the inertial frame (IF) and the auxiliary geographical frame (AGI) is derived in a geometric manner. Second, a model predictive method is used to judge whether the constraint of the no-fly zone is activated in AGI. Then, additional bank reversal is performed to shape the entry trajectory at the right time so as to avoid the no-fly zone. This method is very easy to be implemented onboard and does not increase the additional computational burden. The nominal and Monte Carlo simulations are conducted to show that the proposed method consistently offers very great, stable, and robust performances. INDEX TERMS Autonomous no-fly zone avoidance, entry guidance, linear pseudospectral model predictive control.
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