The Variable Structure Control Of Some Biological Dynamic Systems

With the growth of population, urbanization and the progress of technology, more ecological environments are changed rapidly. For example, the over-exploitation of natural resources and deterioration of environmental pollution, the sustainable development of ecosystem is being confronted challenge. Therefore, rational exploitation and utilization of natural resources is hot topics. As a synthetical method of system control, variable structure control has some advantages, such as simple algorithm, stronger robust, and the higher reliability. It is these characteristics that variable structure control has been applied in many fields. But there is fewer applications in biological systems. In this paper, variable structure control is introduced to some biological systems. The main work is as follows:(1) The pole assignment of linear systems and the method of Lyapunov functions are employed to investigate the variable structure control of the model of endocrine eisrupt system or diethylstibestrol transferring in the human body. The variable structure controllers which make the system reach stable point faster than before are obtained. That makes the time of diethylstibestrol in body short. This method decreases diethylstilbestrol hurt for human body.(2) Using the theory of variable structure control, the variable structure control for the model of phytoplankton and zooplankton based on nutrition kinetics is investigated. The variable structure controllers is designed to make the system stable at positive equilibrium as fast as possible. These studies are helpful for the synthetical control of biological systems.(3) Based on nutrition dynamics, the model of a singular predator-prey-residual system is proposed. Using the theory of variable structure control, the variable structure control of the model is investigated. The controller which makes the system stable and sustainable is obtained. Futhermore, using singular system theory, the stability and the regularility of the model are studied, and the sufficient conditions of the stability and the regularility for the system in question are given.In each part, besides theoretical analysis, simulations are done to check the rationality and feasibility of the theories.