Constrained data smoothing via optimal control
Abstract
The article considers a problem of best smoothing in a strip, where the objective is to find a function that satisfies bilateral constraints on its values, for all and minimizes a weighted sum of the ‐norm of the second derivative and squared deviations from specified values, , at discrete points . We assume that constraints and are continuous functions that are linear in each interval , . We connect this problem to a state‐constrained optimal control problem for the double integrator, and give conditions for the existence and uniqueness of the solution under which we also show that the solution is a cubic spline with knots at and no more than two additional knots in each interval . We propose a numerical algorithm for solving this problem based on a two stage minimization, where the outer loop optimization problem is finite‐dimensional and convex, while the inner loop optimization problem admits a solution which is easy to compute. Numerical results that show the efficacy of the proposed approach are reported.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Apr 02, 2022
- Source ID
- 10.1002/oca.2890
Entities
People
- Assen L. Dontchev
- Ilya V. Kolmanovsky
- Trung B. Tran
Organizations
- Air Force Office of Scientific Research
- University of Michigan