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

[摘要] This thesis presents the implications of using adaptive time-stepping schemes with the adjoint-state method, a widely used algorithm for computing derivatives in optimal-control problems. Though we gain control over the accuracy of the timestepping scheme, the forward and adjoint time grids become mismatched. Despite this fact, I claim using adaptive time-stepping for optimal control problems is advantageous for two reasons. First, taking variable time-steps potentially reduces the computational cost and improves accuracy of the forward and adjoint equations;; numerical solution. Second, by appropriately adjusting the tolerances of the timestepping scheme, convergence of the optimal control problem can be theoretically guaranteed via inexact Newton theory. I present proofs and computational results to support this claim.

[发布机构] Rice University