Preprint
Bernstein approximation of optimal control problems
ArXiv.org
12/14/2018
Abstract
Bernstein polynomial approximation to a continuous function has a slower rate
of convergence as compared to other approximation methods. "The fact seems to
have precluded any numerical application of Bernstein polynomials from having
been made. Perhaps they will find application when the properties of the
approximant in the large are of more importance than the closeness of the
approximation." -- has remarked P.J. Davis in his 1963 book Interpolation and
Approximation. This paper presents a direct approximation method for nonlinear
optimal control problems with mixed input and state constraints based on
Bernstein polynomial approximation. We provide a rigorous analysis showing that
the proposed method yields consistent approximations of time continuous optimal
control problems. Furthermore, we demonstrate that the proposed method can also
be used for costate estimation of the optimal control problems. This latter
result leads to the formulation of the Covector Mapping Theorem for Bernstein
polynomial approximation. Finally, we explore the numerical and geometric
properties of Bernstein polynomials, and illustrate the advantages of the
proposed approximation method through several numerical examples.
Details
- Title: Subtitle
- Bernstein approximation of optimal control problems
- Creators
- Venanzio CichellaIsaac KaminerClaire WaltonNaira HovakimyanAntonio Pascoal
- Resource Type
- Preprint
- Publication Details
- ArXiv.org
- ISSN
- 2331-8422
- Language
- English
- Date posted
- 12/14/2018
- Academic Unit
- Mechanical Engineering
- Record Identifier
- 9984201436902771
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