Optimal Linewise Control Of Dam-detouring Osmtic System For Concrete Dams With Heterogemous

This doctoral dissertation discusses the rockery part's seepage system control of large concrete dams which has always been a problem for the construction department. It raises special attention of the designers, administrative officials, and inhabitants in dam area for it concerns the safe operation of the dam. So the following dissertation has its practical meaning.One of the solutions is to set drainage system between the rock and its neighboring part, which are quite different in their nature. The drainage system is composed of groups of drainage pores which dispose the seepage water in rockery dam and its neighboring parts to reduce the osmotic pressure and buoyant force, preventing the damage caused by over seepage flow so as to ensure the safety of the dam. Firstly the dissertation sets up the mathematics mode of optimal control of the rockery part's seepage system which is the optimal linewise control of the system governed by the first and second boundary value hybrid problem for tri-dimension discontinuous coefficient's second order elliptic partial differential equations. It provides the study framework for the solution to the seepage problem by effective use of partial differential equations and modern theory and its methods of optimal control. The mode in this dissertation is more practical than the precedent research, therefore it raises some new challenges in mathematics and control theory, which is mainly discussed in Chapter II.Secondly, with the theory and methods of partial differential equation, this dissertation proves generalized solutions for the state equation of mathematical mode and the existence and uniqueness of the regularity of adjoint state equation, laying the mathematical theoretical foundation for the discussion of seepage system control, which is illustrated in Chapter III and IV.Thirdly, with optimal control and method of J.L.Lions, Chapter V and VI deals with optimal linewise control of second cost functional, proves the existence, uniqueness of the optimal control and its necessary conditions, and finally obtains the op-timality system. And with Penalty Shifting method, it structures the approximate program of optimal control value and proves the convergence of the method on appropriate Hilbert spaces. It provides the effective means for the practical solution to the problem of seepage control.The main innovation of this dissertation as follows:(1) It builds the new mathematical model on rockery dam and its neighboring parts which have different nature. In its state equation, the coefficient is discontinuous, and the first and second boundary value is hybrid, which is more practical than the precedent research, therefore it raises some new opportunities and challenges in mathematics and control theory.(2) The defining the solution to the state equation and proving its existence and uniqueness must be based on the regularity of generalized solution of hybrid problem in adjoint state equation, which hasn't been discussed and solved in the precedent mathematical literature. With prior estimate theory, it proves the existence anduniqueness of regularity of solution, which not only proves the uniqueness of the solution of adjoint state equation, but also provides the theoretical foundation for the further study in control theory, making a minor contribution for the development of the regularity theory of partial differential equation.(3) With Penalty Shifting method, it structures the approximate program of optimal control value and proves the convergence of the method on appropriate Hilbert spaces. It provides the effective means for the practical solution to the problem of seepage control. By utilizing the Lagrangt multiply number approximate method in Shifting theory, the original coefficient in Penalty Method is constant, and it won't increase infinitely and even become infinite in the further calculations, while the ufc remains finite. It largely reduces the calculation in the Pure Penalty Method proposed by H.C.Lee and Y.Choi in their research paper in the famous American journal J.Math.Anal.Appl., 2000 edition(SCI ). (Since their Pure Penalty Method has no Largrange multiply number approximate u/., and only has the Penalty coefficientc* = — e^ —> 0, Ck -? +oo).