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.

翻译：本文提出将复合伯恩斯坦多项式作为一种直接配点法，用于逼近最优控制问题。我们分析了复合伯恩斯坦多项式的收敛特性，并讨论了其在求解最优控制问题时具备的优越性质。通过一个Bang-Bang控制实例验证了所提逼近方法的有效性。最后，我们将该方法应用于运动规划问题，给出了强调本方法解决复杂最优控制问题能力的实用解决方案。