Identification And Optimal Control Of Distributed Parameter System: Theory Algorithm And Application

This dissertation studies mainly the identification and the optimal control problem in parabolic PDEs, including the existence of solutions of state equations and optimal solutions of the optimal control and the identification problems, optimality conditions, the relation between the state functions and the control functions (identification parameters), the algorithms of infinite-dimensional optimization problems deriving from the identification and the optimal control problem of distributed parameter system. The main results, obtained in this dissertation, may be summarized as follows:1. The identification problem of thermal parameters in the paleotempture field equation is reported. On some reasonable assumptions, the existence and the uniqueness of the solution of partial differential equation are proved by using the semigroup theory; then based on the current basin temperature from the practical survey, the mathematical model about the identification problem is established, and the identifiability and the existence of the optimal solution of the identification problem are proved; in terms of the adjoint method presented by Chavent, the optimality condition of the identification problem is given; finally the corresponding algorithm is devised.2. Nonlinear source term identification problem about a quasilinear parabolic heat equation is investigated. For the given function determined, the existence and the uniqueness of the solution of the state equation are proved and the dependence of the solution of the state equation on the identification parameter is discussed; then the identifiability is verified; through choosing suitable basic functions, the above identification problem can be transformed into a constant coefficients identification problem; and an practical iterative algorithm for solving the identification problem is presented, the feasibility and validity of the algorithm is verified by the numerical experiments.3. Two parameter identification problems described by coupled dynamical system are investigated. Firstly, the identification of the double medium system is considered, the existence, the uniqueness and the boundness of the solution of the system of the partial differential equations are proved by using the monotone method, the mathematical model of the parameter identification problem is established, and under some mild assumptions, the optimality system about the identification is derived, thus the suitable gradient methods can be employed to solving the identification problem. Secondly, the theories of optimal control of distributed parameter system are introduced to investigate the parameters identification problem involving the three-dimensional population system. The existence and uniqueness of the parameter identification problem are established, and the continuous dependence and Gateaux differentiability of the solutions of the state equations on the identified parameters are presented, and the optimality condition characterized by the system equations, the adjoint equations and the variatiorialinequality simultaneously is derived by introducing adjoint variables.4. The algorithm solving an optimal control problem governed by a semilinear parabolic equation with the control in the coefficients and source term is studied. The strong variational method which presented by Mayne to solve the optimal control of lump parameter system is developed to semilinear parabolic optimal control problem. The conclusion which, for a given non-extremal admissible control, another admissible control can be constructed such that the corresponding value of the objective functional decreases is proved, based on the result, an optimality condition is obtained and the strong variational method which solves optimal control problem is presented and the associated convergence result is proved also.5. The optimal control problems governed by the Navier-Stokes and a system of parabolic equations with state and control constraints are studies respectively. Firstly, the existence of th...