Analysis And Control About A Kind Of Food Chain Model

In real life, most of the control systems have nonlinear characteristics, and inevitably, they have some disturbance factors from interior or outside of the system in the actual operation. Thus the system may deviate from original working position. If we want it running as usual, we must redesign the system. In this paper, we study on the the asymptotical stable of a kind of utility nonlinear control system, give out control law based on nonlinear control theory and combine the new development of mathematics—Sum-of-Squares (SOS) optimization algorithm, these two ways can make the system stability.Food-chain system is a regenerate resource. Its rational exploitation and utilization are given more and more attention of scholars. And they have achieved certain results. A lot of biotic environment can be seen as food-chain systems in reality. This model of food-chain system can be similar used to real life in many ways. For example:in medicine, the characteristics of food-chain system can be used to manufacture some medicines to improve human organism and strengthen human capacity to resist disease; in agriculture and environmental protection, the characteristics of food-chain system can be used in pest control and sewage treatment. In this paper, we firstly give out the model which would be study and the exist condition of the equilibrium. Then analyze the stabilityof every equilibrium points. Lastly by using nonlinear control theory and SOS optimization algorithm, we studied the asymptotical stability of the equilibrium in this kind of food-chain system (nonlinear control theory from a given output to construct control law, which can make the system as exact linearization system or zero dynamics system. SOS optimization algorithm is about adding proper control law to the system, then directly stable its). By adding controller to the system at the unstable points, namely by harvest or put in living things, we get the controller laws which made the system asymptotically stable around the equilibrium points, achieve the asymptotical stable’s aim. At the same time, the SOS optimization algorithm gives it DOA.