The Study Of Optimal Control And Optimization Control For The Management Models Of Fishery

With the biological overfishing, the fish resources storage is influenced and the marinebiodiversity is destroyed. As a renewable resource, the rational exploitation and utilization offish resources attract the attention of scholars. In the view of biology and economics, severalmanagement models of fishery are built up. Using the principle of optimal impulsive controland the principle of optimization impulsive control, the management of fishery is studied toobtain the impulsive harvest time and corresponding harvest level which make the sustainableutilization of fish resource and fishman get maximum economic benefit. The main contents ofthis paper are as follows:Firstly, on the basis of a single-species model with Logistic growth, the objectivefunction with discount rate is given. And the management model of fishery is got. Using theprinciple of optimal impulsive control, the controller which makes fishman get maximumeconomic benefit is designed to get the optimal impulsive harvest time and the correspondingharvest level. The objective function with discount rate shows the sustainable development offish resources.Secondly, on the basis of a single-species model with Logistic growth, the managementmodel of fishery with continuous harvest and impulsive harvest is proposed. According to theprinciples of economics, a reasonable objective function is given. Using the principle ofoptimal impulsive control, on the one hand, for the continuous harvest, the optimal switchtime and the corresponding population level which make fishman get maximum economicbenefit are obtained; on the other hand, for the impulsive harvest, the optimal harvest timeand the corresponding harvest level are got. By the principle of optimization impulsivecontrol, the corresponding harvest time and the harvest level which make the sustainableutilization of fish resources are got. Combing the principles above, the conditions which canensure the fishman to get the maximum economic benefit and the sustainable development offish resource are obtained.Thirdly, on the condition of the same economic profit, the residual amount of fishresources with two impulsive effects is larger than the one with an impulsive effect. Based onthe principles of ecology and economics, the management model of fishery with twoimpulsive harvest is given. Using the principle of optimal impulsive control and the principleof optimization impulsive control, the harvest time and the corresponding harvest level which make fishman get maximum economic benefit and the sustainable development of fishresource are obtained.