Time domain decomposition methods for second-order linear quadratic optimal control problems

Abstract

Optimal control problems governed by time-dependent differential equations lead to large scale problems. Their numerical solution is challenging due to large storage demands resulting from the coupling in time of the solution of the governing (state) equation and the so-called adjoint equation. This thesis investigates two time-domain decomposition based methods for the solution of linear quadratic control problems governed by second order differential equations. Both methods deal with storage requirements by reformulating the problem so that some of the variables at time subdomains are expressed as implicit functions of others; through the solution of a local state equation or control subproblem. The methods differ in the variables that are being eliminated and, more importantly, in the transmission conditions that link the subproblems at time interfaces. This work exposes the connections between formulations, extends algorithmic approaches for the second formulation, and compares numerically the performance of each method