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A Fast Nonlinear Model Predictive Control Method Based on Discrete Mechanics

机译：基于离散力学的快速非线性模型预测控制方法

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Nonlinear Model Predictive Control (NMPC) is an advanced control technique that often relies on a computationally demanding optimization problem and numerical integration algorithms. This paper proposes and investigates a novel method with less computational effort to improve the efficiency of NMPC using a formulation based on discrete mechanics (DM). In contrast to classical NMPC formulations, the proposed method merges the two stages, for solving both the initial value problem (IVP) for prediction as well as the nonlinear programming problem (NLP) for optimization, into a single stage for solving an optimal boundary value problem (BVP) using NLP techniques. By exploiting the structural features of DM a symbolic solution set of the equations of motion are derived offline on each discretization node along the whole optimization horizon. Within an NLP, the optimal solution is efficiently obtained online under the consideration of the boundary constraints. As a benchmark, the widely used NMPC formulation based on direct multiple shooting (MS) method is served to assess the convergence and the excellent real-time performance of this method. The closed-loop performance is demonstrated by the swing-up of an unstable numerical experiment.
机译：非线性模型预测控制（NMPC）是一种先进的控制技术，通常依赖于计算要求苛刻的优化问题和数值集成算法。本文提出并研究了利用基于离散力学（DM）的制剂来提高NMPC效率的计算努力的新方法。与古典NMPC制剂相比，所提出的方法合并两个阶段，用于解决预测的初始值问题（IVP）以及用于优化的非线性编程问题（NLP），以求解最佳边界值的单个阶段问题（BVP）使用NLP技术。通过利用DM的结构特征，沿整个优化地平线的每个离散化节点在每个离散节点上导出运动方程的符号解决方案集。在NLP中，最佳解决方案在思考边界约束下有效地在线获得。作为基准测试，基于直接多拍摄（MS）方法的广泛使用的NMPC配方用于评估该方法的收敛性和优异的实时性能。通过不稳定的数值实验的摆动来证明闭环性能。

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