The Stability Of Solutions And Optimal Control Of Sea-Ice Thermodynamic System

Based on the temperature field of Artic sea-ice,we established the snow-ice-water coupling pattern to study the thermodynamic process of the artic sea-ice.Taking the temperature of snow,ice and water layers as state variables,and the density,specific heat, coefficients of heat conduction and the parameters of thermodynamic practical equations as control variables,we construct a parabolic distributed system of snow-ice-water coupling pattern.The aim for researching the Arctic sea ice is that the solution of the dynamical system should approximate the corresponding measured values as better as possible.Taking this aim, an optimal control system is established based on the nonlinear dynamic system.The properties of this optimal control system are then studied.In Chapter 1,the developing process of control theory,the present study of Arctic sea ice is reviewed.The main work of this dissertation is also introduced in this chapter.We present the preliminary knowledge in Chapter 2,which includes the main properties of Sobolev Functional Space,the calculus on the Banach Space and the existence and uniqueness of the solutions of parabolic equations.Chapter 3 and Chapter 4 present the main results of this dissertation,which can be summarized as follows:1.The parabolic distributed parameter system of snow-ice-water coupling pattern and parametric identification optimal control model is established.2.By dividing the parabolic distributed system,we studied the existence and uniqueness of the solutions of the nonlinear dynamic system.Its stability is also discussed.3.The existence of the optimal solution of the optimal control model is studied.