| The optimal control problem of population dynamics is an active field in control theory. Its abundant theories and advanced methods provide powerful and fruitful tools for solving control problems in the fields of science and technology, and it contributes to the work of population system development and control. Considering the weighted size in population system, the optimal control problems for two classes of non-linear population system with fertility and mortality depending on age and weighted size are given. We also do some research about the problem of the optimal control for a class of age-dependent population system based on weighted size. According to the contents, this paper is divided into three chapters.In the first chapter, we give the preface. It introduces the background, the present studying of population dynamics at home and abroad and the preparative theory.In the second chapter, on the basis of analyzing and summarizing the optimal control problems of modern population dynamics, considering the influence of age-dependence and the weighted size, this paper constructs the model with the form of differential-integral equations. By means of characteristic line, Gronwall Lemma, Bellman Theory, Fatou Lemma, Ekeland's variational principle, the Banach fixed the point theory, adjoint system and so on, the problem of the optimal control for a class of age-dependent population system based on weighted size is discussed systematically, the existence and uniqueness of the harvest control of the differential-integral equations is proved, the necessary conditions of optimal control problem is obtained.In the third chapter, it is about the optimal control for a class of periodic age-dependent population system based on weight, the adjoint system of the model is analyzed, the continuity properties of the system solution in terms of the control variable is certificated, and the necessary conditions of optimal control problem is obtained.
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