Time–Domain Decomposition Iterative Methods for the Solution of Distributed Linear Quadratic Optimal Control Problems

We study a class of time–domain decomposition based methods for the solution of distributed linear quadratic optimal control problems. Our methods are based on a multiple shooting reformulation of the distributed linear quadratic optimal control problem as a discrete–time optimal control (DTOC) problem in Hilbert space. The optimality conditions for this DTOC problem lead to a linear system with block structure. This motivates the application of block Gauss–Seidel methods for its solution. We show that certain instantaneous control techniques can be viewed as the application of one step of the forward block Gauss–Seidel method applied to the DTOC optimality system. To obtain better convergence properties, we imbed the block Gauss–Seidel methods as preconditioners in a Krylov–subspace method.