The dynamic logic-based switched system is an important hybrid system formed by the coupling of continuous state subsystem and logical dynamic subsystem.It has important applications in characterizing the complex behavior of the system,supervisory control and adaptive control.Due to the hybrid nature of states,that is,there are both logical and continuous states,the analysis and design of such hybrid systems cannot be carried out under a unified framework based on existing methods.In this thesis,based on the matrix semi-tensor product and the vector representation theory of logic,the control problem of discrete-time switched system based on dynamic logic is studied.Using the hybrid state merging technique and Lyapunov stability theory,a method for designing feedback-stabilized switching laws for discrete switched systems based on dynamic logic is presented.Firstly,based on the matrix semi-tensor product and the vector representation of logic,the logic subsystem is transformed into algebraic form.Then,the vector form of the logic state and the continuous state are merged by the semi-tensor product of the matrix,and the dynamic equation of the merged state is derived,which can be regarded as being obtained by limiting the ordinary switched system to an invariant set.By constructing the Lyapunov function of the merged switched system on the invariant set,the method of feedback stabilization of the switched law is obtained.In particular,if the quadratic Laypunov function is used,the design of the feedback-stabilized switching law will be reduced to the solution of a set of bilinear matrix inequalities.The method is also applied to the design of dynamic stabilization switching laws for discrete-time switched systems subject to minimum dwell time constraints.Combining the hybrid state merging technique and the dynamic programming principle,a design method of the optimal control law in the finite time domain based on the dynamic logic discrete-time switched control system is obtained.Compared with ordinary control systems,this kind of control system is characterized by the existence of continuous and logical control inputs in the continuous state subsystem and the logical dynamic subsystem,respectively.By merging the two subsystems,a general switched control system is obtained,in which the control term has bilinearity.Using the quadratic performance index,this thesis deduces the switching law of dynamic programming and the iterative algorithm of the optimal continuous control sequence,and applies the obtained results to the optimal switching control of the power converter.There are 13 figures,6 tables,and 85 citations in this thesis. |