Sensitivity Analysis for Piecewise-Affine Approximations of Nonlinear Programs with Polytopic Constraints
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910471706116096 |
|---|---|
| author | Gharavi, Leila Liu, Changrui De Schutter, Bart Baldi, Simone |
| author_facet | Gharavi, Leila Liu, Changrui De Schutter, Bart Baldi, Simone |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_20387 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Sensitivity Analysis for Piecewise-Affine Approximations of Nonlinear Programs with Polytopic Constraints Gharavi, Leila Liu, Changrui De Schutter, Bart Baldi, Simone Systems and Control Optimization and Control 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. |
| title | Sensitivity Analysis for Piecewise-Affine Approximations of Nonlinear Programs with Polytopic Constraints |
| topic | Systems and Control Optimization and Control |
| url | https://arxiv.org/abs/2405.20387 |