Shooting method-based algorithms for solving control problems associated with second-order hyperbolic partial differential equations

In this thesis, we study some optimal control problems of hyberbolic equations, we extend the mathematic work on this subject. We propose a systematic approach for solving control problems associated with second order hyperbolic PDEs, including proper formulation of cost functions and admissible space, precise constructions of optimal conditions and optimal systems. We discuss the weak solutions arising from nonlinear terms, develop a new algorithm, i.e., a shooting method based algorithm to compute the optimal controls (both distributed control and boundary control), we also implement efficiently other numerical methods, such as Gradient method, abbreviated Newton's method, these methods and implementations can be extended to heat equations, plate equations, etc.

Furthermore, we propose, analyze and implement a new approach for solving the exact boundary controllability problems. Our computational results demonstrate that our algorithms work effectively and they represent legitimate alternatives to those in the extant literature.