Translation, solving scheme, and implementation of a periodic and optimal impulsive state control problem

Abstract

The periodic solution of the impulsive state feedback controls (ISFC) has been investigated extensively in the last decades. However, if the ecosystem is exploited in a period mode, what strategies are implemented to optimize the cost function at the minimal cost? Firstly, under the hypothesis that the system has a periodic solution, an optimal problem of ISFC is transformed into a parameter optimization problem in an unspecified time with inequality constraints, and together with the constraint of the first arrival threshold. Secondly, the rescaled time and a constraint violation function are introduced to translate the above optimal problem to a parameter selection problem in a specified time with the unconstraint. Thirdly, gradients of the objective function on all parameters are given to compute the optimal value of the cost function. Finally, three examples involving the marine ecosystem, computer virus, and resource administration are illustrated to confirm the validity of our approaches.