Optimal Control For One Impulsive Differential System

In some time intervals, many practical problems and systems show the character of continuous system; but at some moments, they show the character of discrete system. Impulsive differential equation is suitable to describe them. In many research fields, impulsive differential equation shows larger prospects of applications. Practice has proved that comparing with continuous control method, impulsive control method is effective and sometimes better in performance.First we introduce several concepts and theorems of impulsive differential equation, including the definition of impulsive differential equation, the definition of solution of impulsive differential equation, and optimal impulsive control theorem based on population dynamic models.Second, in connection with the problem of culture and capture in fishery, we consider two types of biological model of population growth - Logistic model and Gompertz model and do impulsive captures at some fixed moments respectively, i.e., impulsive Logistic capture model and impulsive Gompertz capture model.Finally, we put forward the performance indicator which we will optimize in this paper and call it profit function. By using the results of optimization problems under impulsive differential equations and the theorem of periodic solution of impulsive differential equations, on the premise of sustainable development of fishery, we optimize the two impulsive capture models mentioned before. Furthermore, the optimal impulsive capture time and the corresponding optimal impulsive capture amount of impulsive Logistic capture model are obtained.