Representation and control of infinite dimensional systems (vol. 1)
Representation and control of infinite dimensional systems (vol. 1)
The superlinear convergence behaviour of GMRES
Journal of Computational and Applied Mathematics
On exact and approximate boundary controllabilities for the heat equation: a numerical approach
Journal of Optimization Theory and Applications
Iterative solution methods
Iterative methods for solving linear systems
Iterative methods for solving linear systems
SIAM Journal on Control and Optimization
Numerical Solution of a Flow-Control Problem: Vorticity Reduction by Dynamic Boundary Action
SIAM Journal on Scientific Computing
Circumventing Storage Limitations in Variational Data Assimilation Studies
SIAM Journal on Scientific Computing
Instantaneous control of backward-facing step flows
Applied Numerical Mathematics
Iterative solution of nonlinear equations in several variables
Iterative solution of nonlinear equations in several variables
Practical methods for optimal control using nonlinear programming
Practical methods for optimal control using nonlinear programming
Analysis of instantaneous control for the Burgers equation
Nonlinear Analysis: Theory, Methods & Applications
Nonlinear Equation Solvers in Boundary Value Problem Codes
Proceedings of a Working Conference on Codes for Boundary-Value Problems in Ordinary Differential Equations
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
A spatial domain decomposition method for parabolic optimal control problems
Journal of Computational and Applied Mathematics
Block iterative algorithms for the solution of parabolic optimal control problems
VECPAR'06 Proceedings of the 7th international conference on High performance computing for computational science
Analysis of Block Parareal Preconditioners for Parabolic Optimal Control Problems
SIAM Journal on Scientific Computing
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We study a class of time-domain decomposition-based methods for the numerical solution of large-scale linear quadratic optimal control problems. Our methods are based on a multiple shooting reformulation of the linear quadratic optimal control problem as a discrete-time optimal control (DTOC) problem. The optimality conditions for this DTOC problem lead to a linear block tridiagonal system. The diagonal blocks are invertible and are related to the original linear quadratic optimal control problem restricted to smaller time-subintervals. This motivates the application of block Gauss-Seidel (GS)-type methods for the solution of the block tridiagonal systems. Numerical experiments show that the spectral radii of the block GS iteration matrices are larger than one for typical applications, but that the eigenvalues of the iteration matrices decay to zero fast. Hence, while the GS method is not expected to convergence for typical applications, it can be effective as a preconditioner for Krylov-subspace methods. This is confirmed by our numerical tests.A byproduct of this research is the insight that certain instantaneous control techniques can be viewed as the application of one step of the forward block GS method applied to the DTOC optimality system.