Time-Domain Decomposition Iterative Methods for the
Solution of Distributed Linear Quadratic Optimal Control
Problems
Abstract
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.
Keywords
Linear quadratic optimal control problems, instantaneous control,
suboptimal control, multiple shooting, discrete-time optimal control
problem, Gauss-Seidel method, Krylov subspace methods.
AMS subject classifications
49N10, 49M05, 49M27, 65F10