Variable Structure Control For Stochastic Singular Bio-economic Systems With Markovian Jumps

In recent years,applying the theory of singular systems to biological systems has become a hot topic for many scholars.In practice,the population density will be affected by many random factors,so it is of great academic value and practical significance to study the modeling of stochastic singular biological systems and conduct stability analysis.In this paper,a stochastic singular bio-economic system with Markovian jump is studied by the sliding mode control theory.T-S fuzzy method is used to fuzzy the system,so that it has a certain stability in the ecological environment.The conclusions obtained have a certain application value.The specific work is as follows:(1)The research status of singular biological systems,Marcovian jump systems,observer design and sliding mode variable structure control are introduced.The main research contents of this paper are further expounded.(2)The finite time sliding mode control problem for a class of Markovian jump systems based on observer is studied.A new singular biological system model is established according to Gordon's economic theory.Due to the influence of human activities,mature populations will be affected by a variety of factors when they are captured,leading to varying degrees of impact on the market price of mature populations.Assuming that the market price of the population follows the Markovian jump process,according to the T-S(Takagi-Sugeno)fuzzy rule,A generalized biological system model with Markovian jump can be obtained.Starting from the actual situation,because the measuring equipment and economic limitations on use,not easy to get the internal state of the model,so the design of an observer to realize the state feedback,a sliding mode controller based on observer design,make the error system and the state of the observer system trajectory is drawn from the beginning to the near the sliding surface,and carries on the analysis of boundedness.(3)To solve the variable structure control problem of a class of stochastic singular bio-economic system with Markovian jump,a novel singular bio-economic system model with Markovian jump is established by using Gordon's theory and adding several variables,such as basic cost and loan cost,on the basis of the existing model.Firstly,the singular bio-economic system theory is combined with the T-S fuzzy rule to control the density of the biological population within a bounded range,eliminate some uncertain factors in the system,and design the sliding mode surface.Then,a Lyapunov function is constructed,and a sufficient condition for the mean-square asymptotic admissive of sliding modes is given.Finally,an integral sliding mode controller is constructed to make the system state trajectory be driven to the sliding mode plane in a finite time,and remain on the sliding mode plane in the following time.