Stability Of Point Control And Optimality Of Distributed Control Of Timoshenko Beam

In recent decades,the stability analysis and optimal control of elastic systems have been paid more and more attention.As an elastic system,beam system plays an important role in many fields,especially the Timoshenko beam model,which is widely used in aeronautical spacecraft components and robot arms,and has many advantages.Therefore,it is significant to study the stability and optimality of Timoshenko beam system.In this thesis,the energy attenuation of Timoshenko beams with the control of series deformation and the optimality of distributed control are studied.On the one hand,for the energy attenuation of Timoshenko beams,firstly,the polynomial stability of the system is proved by using the semigroup theory of linear operator.Then,the discrete form of energy decay of the system is given by the shape function method.On the other hand,for the optimality of Timoshenko beams with distributed control,the system optimality is obtained by using rolling time domain combined with dynamic programming.This thesis is divided into five parts:In the first part,the background and development of the stability and optimality of elastic systems are briefly introduced.Then,the research background of this paper is described.Finally,the main research contents,theoretical methods and results are presented.In the second part,some basic concepts,theories,methods and some important inequalities used in this paper are introduced,which are used to provide the theoretical basis for the study of the stability and optimality of the system.In the third part,the following system is proved by using the semigroup theory of linear operator.(?)It is polynomial stable,and the discrete form of energy attenuation of the system is obtained by using the shape function method.In the fourth part,dynamic programming combined with multiplier technique is used to study the optimal control problem of the following systems with the aid of dual systems.(?)In the fifth part,the contents of this paper are summarized briefly,and the future development direction is prospected.