18 research outputs found
A Comparative Study of Sensitivity Computations in ESDIRK-Based Optimal Control Problems
In this paper, we compare the impact of iterated and direct approaches to
sensitivity computation in fixed-step explicit singly diagonally-implicit
Runge-Kutta (ESDIRK) methods when applied to optimal control problems (OCPs).
We use the principle of internal numerical differentiation (IND) strictly for
the iterated approach, i.e., reusing the iteration matrix factorizations, the
number of Newton-type iterations, and Newton iterates, to compute the
sensitivities. The direct method computes the sensitivities without using the
Newton schemes. We compare the impact of the iterated and direct sensitivity
computations in OCPs for the quadruple tank system. We benchmark the iterated
and direct approaches with a base case. This base case is an OCP that applies
an ESDIRK method that refactorizes the iteration matrix in every Newton
iteration and uses a direct approach for sensitivity computations. In these
OCPs, we vary the number of integration steps between control intervals and we
evaluate the performance based on the number of SQP and QPs iterations, KKT
violations, and the total number of function evaluations, Jacobian updates, and
iteration matrix factorizations. The results indicate that the iterated
approach outperforms the direct approach but yields similar performance to the
base case.Comment: 6 pages, 5 figures, 2 tables. Submitted for European Control
Conference 2024 (ECC2024). Stockholm, Swede