Time Optimal Control Of System Governed By Integro-Differential Equations And Meyer Approximation Of Time Optimal Control On Infinite Dimensional Spaces

In this thesis, we pay great attention to discuss the existence of time optimal control of system governed by a class of semi-linear integro-differential equations and Meyer Approximation of time optimal control of system governed by semi-linear equations and nonlinear equations respectively on infinite dimensional Banach spaces.First, the following control system governed by semi-linear integro-differential equations (7) is consideredwhere A is the infinitesimal generator of a Co-semigroup, I = [0,1] and l is fixed and integro operator is given byAfter getting the extisence of mild soultion of equations (7), we pay great attention to study the existence of time optimal controls about the target which are corresponding to a fixed point and a set varying with time respectively. As conclusion, we obtain two new existence results.Second, another remarkable problem that Meyer approximation of time optimal control of system governed by semi-linear equationsand nonlinear equationsare also investigated respectively on infinite dimensional Banach spaces.Using the uniformly operator topology of compact semigroup theory and transformation idea, a sequence of solution of Meyer problems are constructed to approach to a class of time optimal control problems of system governed by semi-linear equations (8) on infinite dimensional Banach spaces. A deep relation between Meyer problem and time optimal control is also presented. Consequently, the existence of time optimal control is obtained. Here, operator B satisfies relative weak conditions such as B satisfies essence bounded.By virtue of the strongly operator topology of Co-semigroup theory and transformation idea, a sequence of solution of Meyer problems are constructed to approach to a class of time optimal control problems of system governed by nonlinear equations (9) on infinite dimensional Banach spaces. A deep relation between Meyer problem and time optimal control is also presented. Consequently, the existence of time optimal control is obtained. Though Co-semigroup is not as strong as compact semigroup, B satisfies relative strong condition such as B satisfies essence bounded and it is a strong continuous operator.