Journal article
Consistency of Approximation of Bernstein Polynomial-Based Direct Methods for Optimal Control
Machines (Basel), Vol.10(12), p.1132
11/28/2022
DOI: 10.3390/machines10121132
Abstract
Bernstein polynomial approximation of continuous function has a slower rate of convergence 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.”—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 and can be used for costate estimation of the optimal control problems. This 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
- Consistency of Approximation of Bernstein Polynomial-Based Direct Methods for Optimal Control
- Creators
- Venanzio Cichella - University of IowaIsaac KaminerClaire WaltonNaira HovakimyanAntónio Pascoal
- Resource Type
- Journal article
- Publication Details
- Machines (Basel), Vol.10(12), p.1132
- DOI
- 10.3390/machines10121132
- ISSN
- 2075-1702
- eISSN
- 2075-1702
- Language
- English
- Date published
- 11/28/2022
- Academic Unit
- Mechanical Engineering
- Record Identifier
- 9984353741902771
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