Optimal Control using Composite Bernstein Approximants

TL;DR

This paper introduces composite Bernstein polynomials as a novel direct collocation method for solving optimal control problems, demonstrating convergence, beneficial properties, and practical effectiveness through examples.

Contribution

It presents a new approximation approach using composite Bernstein polynomials for optimal control, including convergence analysis and application to complex problems.

Findings

Effective in solving bang-bang control problems

Demonstrates convergence properties of the method

Successfully applied to motion planning tasks

Abstract

In this work, we present composite Bernstein polynomials as a direct collocation method for approximating optimal control problems. An analysis of the convergence properties of composite Bernstein polynomials is provided, and beneficial properties of composite Bernstein polynomials for the solution of optimal control problems are discussed. The efficacy of the proposed approximation method is demonstrated through a bang-bang example. Lastly, we apply this method to a motion planning problem, offering a practical solution that emphasizes the ability of this method to solve complex optimal control problems.