Approximation methods and spatial interpolation in distributed control systems

We propose an approximation method to solve large-scale optimal control problems for spatially distributed systems. The finite-section method is employed to construct finite-dimensional approximations to the large-scale optimal control problem. Then, we study the limit behavior of the approximation method and show that the solution of the approximate problems converge strongly to the solution of the large-scale problem. These techniques are applied to design finite-dimensional local optimal controllers. Finally, a spatial interpolation method is proposed that can patch all locally designed controllers to construct a parameterized family of stabilizing controller for the spatially distributed system. Furthermore, we characterize the class of stabilizing controllers which have finite supports.