The Effects of Coupling Adaptive Time-Stepping and Adjoint-StateMethods for Optimal Control Problems

[摘要] This thesis presents the implications of using adaptive time-stepping schemeswith the adjoint-state method, a widely used algorithm for computing derivativesin optimal-control problems. Though we gain control over the accuracy of the timesteppingscheme, the forward and adjoint time grids become mismatched. Despitethis fact, I claim using adaptive time-stepping for optimal control problems is advantageousfor two reasons. First, taking variable time-steps potentially reduces thecomputational cost and improves accuracy of the forward and adjoint equations'numerical solution. Second, by appropriately adjusting the tolerances of the timesteppingscheme, convergence of the optimal control problem can be theoreticallyguaranteed via inexact Newton theory. I present proofs and computational results tosupport this claim.

[发布机构] Rice University

[效力级别] Mathematics