تقرير
Tightly Bounded Polynomials via Flexible Discretizations for Dynamic Optimization Problems
| العنوان: | Tightly Bounded Polynomials via Flexible Discretizations for Dynamic Optimization Problems |
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| المؤلفون: | Vila, Eduardo M. G., Kerrigan, Eric C. |
| سنة النشر: | 2024 |
| المجموعة: | Computer Science Mathematics |
| مصطلحات موضوعية: | Mathematics - Optimization and Control, Electrical Engineering and Systems Science - Systems and Control |
| الوصف: | Polynomials are widely used to represent the trajectories of states and/or inputs. It has been shown that a polynomial can be bounded by its coefficients, when expressed in the Bernstein basis. However, in general, the bounds provided by the Bernstein coefficients are not tight. We propose a method for obtaining numerical solutions to dynamic optimization problems, where a flexible discretization is used to achieve tight polynomial bounds. The proposed method is used to solve a constrained cart-pole swing-up optimal control problem. The flexible discretization eliminates the conservatism of the Bernstein bounds and enables a lower cost, in comparison with non-flexible discretizations. A theoretical result on obtaining tight polynomial bounds with a finite discretization is presented. In some applications with linear dynamics, the non-convexity introduced by the flexible discretization may be a drawback. |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2403.07707 |
| رقم الأكسشن: | edsarx.2403.07707 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |