2024/05/30 by Leila Gharavi, Changrui Liu, Bart De Schutter +1
Engineering · Computer Science · Mathematics · #eess.SY #cs.SY #math.OC
paper · pdf · doi:10.1109/lcsys.2024.3408711
published as IEEE Control Systems Letters, vol. 8, pp. 1271-1276, 2024 · 6 pages, 4 figures, accepted for publication in IEEE Control Systems Letters
arxiv created 2024/05/30 · arxiv updated 2026/07/31
Nonlinear Programs (NLPs) are prevalent in optimization-based control of nonlinear systems. Solving general NLPs is computationally expensive, necessitating the development of fast hardware or tractable suboptimal approximations. This paper investigates the sensitivity of the solutions of NLPs with polytopic constraints when the nonlinear continuous objective function is approximated by a PieceWise-Affine (PWA) counterpart. By leveraging perturbation analysis using a convex modulus, we derive guaranteed bounds on the distance between the optimal solution of the original polytopically-constrained NLP and that of its approximated formulation. Our approach aids in determining criteria for achieving desired solution bounds. Two case studies on the Eggholder function and nonlinear model predictive control of an inverted pendulum demonstrate the theoretical results.