The Analysis Of Boolean Control Networks Based On L_p-Gain Theory

The stabilization and stability of Boolean(control)network has been the hot spot in control theory recently.By using a tool named semi-tensor prod-uct we can transfer the Boolean(control)network to an algebraic form.This makes our research to be much easier.My thesis devotes to analyzing the stabilization and gain problem of Boolean(control)network simultaneously.Proposing the definition of the lp gain of Boolean(control)network we study state feedback stabilize controller designing problem of Boolean(control)net-work,whose validity is proved by a complicated numerical example.The whole article is divided into five chapters:Chapter One introduces the background and current situation of Boolean(control)network's stability and stabilization and disturbance decoupling and gain problem.By the way this part states the main work of this thesis.Chapter Two describes mainly the basic concepts and properties of Boolean(control)network and semi-tensor product,which is the preliminary of the later three chapters.Further more in this chapter we discuss the applications of the former problems,for example,the algebraic expression of the Boolean(control)networks.Chapter Three considers the state-feedback-control problem and stabliza-tion problem of Boolean(control)network based on the analysis of the above.Here we introduce the Lyapunov conditions for Boolean(control)network's globally asymptotically stable,due to which we give a numerical example to show the design of the state feedback controller for Boolean(control)network.Last but not least we consider Boolean(control)network's l1-gain problem with control input and disturb input the same time.Firstly,we transfer this Boolean network to its algebraic form by semi-tensor product,after deforma-tion operation we get an ordinary Boolean control network.Then we split the structure matrix and.substitute it into the above Boolean control network thus converting the mentioned problem to a common Boolean network's situation.Chapter Four is the generalization of the former chapter.First we intro-duce the concept of energy function proposed by[20],following its method for defining the gain norm we propose the definition of lp-gain,in fact,redefine the gain norm.Then we analyze the state feedback control problem based on this lp-gain theory,and give the sufficient and necessary conditions of the existence of controller through theorem proving.Finally we give a complete algorithm,and validate the theory and method mentioned above by a relative-ly sophisticated numerical case,whose result shows that the algorithm is well defined.Chapter Five is the summery chapter of the whole thesis.We retrospect the main work and innovation points of this dissertation,and summarize the shortcomings and some parts waited for further expanding analysis,which give ideas about the directions and attention-deserved points for the author of this paper.