Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 1271-1276 |
| Number of pages | 6 |
| Journal | IEEE Control Systems Letters |
| Volume | 8 |
| DOIs | |
| Publication status | Published - 2024 |
Bibliographical note
Green Open Access added to TU Delft Institutional Repository 'You share, we take care!' - Taverne project https://www.openaccess.nl/en/you-share-we-take-careOtherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.
Keywords
- Convex functions
- Function Approximation
- Indexes
- Linear programming
- Max-Min-Plus-Scaling Systems
- Non-Convex Nonlinear Programming
- Optimization
- Perturbation Analysis
- Perturbation methods
- Piecewise-Affine Functions
- Predictive control
- Sensitivity analysis
