Sliding Mode Variable Structure Control For A Class Of T-S Fuzzy Singular Biological Systems

Biomathematics is a combination of mathematics and biology.It has been established and completed its own theoretical system in the process of application,and developed various of unique mathematical methods which adapted to the characteristics of biology.In this paper,we abstract the practical problem and combine the invasion of alien species to set up a generalized biological mathematical model,which is considered with the aid of mathematical theory.The research results of this paper can make some contributions to the development of ecological environment.This paper introduces a class of generalized biological economic system with stage structure,which is studied by the T-S fuzzy method.The population density and stability of this class of biological ecosystem are investigated under the consideration of invasion of alien species.Specific work is as follows:(1)Firstly,the background and research actuality of singular systems are introduced,especially the development of singular bio-systems.Then the application and development of sliding mode control and observer design are reviewed.Finally,the main content of this paper is presented.(2)In this paper,we consider the invasion of alien species and sliding mode controller(SMC)design for singular bio-economic systems.Based on the T-S fuzzy control theory,T-S fuzzy biological model with uncertainties is established.By designing the fuzzy integral sliding mode surface,SMC is derived to ensure the accessibility of the model system,which yields a sufficient condition for the global asymptotic stability of the sliding motion.Finally,an example of crayfish infestation demonstrates the validity of the results.(3)It is difficult to measure the population density of invasive species and the error of obtained data is large.In this paper we study the control problem of singular biological economic system based on sliding mode observer(SMO).Firstly,the SMO is designed based on the control input and measurement output.Then the integral sliding mode surface of the error system and the SMO system is established.The admissibility of the system is proved by using LMI method and Lyapunov stability theory.Finally,a sliding mode controller is designed to ensure the accessibility of the constructed system.A practical example of water hyacinth flooding is simulated to verify the validity of the results.