This article tackles the decentralized near-optimal control problem for the class of nonlinear polynomial interconnected system based on a shifted Legendre polynomials direct approach. The proposed method converts the interconnected optimal control problems into a nonlinear programming one with multiple constraints. In light of the formulated NLP optimization, state and control coefficients are used to design a nonlinear decentralized state feedback controller. Overall closed-loop system stability sufficient conditions are investigated with the help of Grönwall lemma. The triple inverted pendulum case is considered for simulation. Satisfactory results are obtained in both open-loop and closed-loop schemes with comparison to collocation and state-dependent Riccati equation techniques.

本文基于移位Legendre多项式直接方法，解决了非线性多项式互联系统的分散近最优控制问题。所提出的方法将相互联系的最优控制问题转换为具有多个约束的非线性规划问题。根据制定的NLP优化，状态和控制系数可用于设计非线性分散状态反馈控制器。借助Grönwall引理研究了整体闭环系统稳定性的充分条件。考虑采用三重倒立摆情况。与配置和状态相关的Riccati方程技术相比，在开环和闭环方案中均获得了令人满意的结果。