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首页> 外文会议>IEEE International Conference on Intelligent Engineering Systems >On Replacing Lagrange’s 'Reduced Gradient Algorithm' by Simplified Fixed Point Iteration in Adaptive Model Predictive Control
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On Replacing Lagrange’s 'Reduced Gradient Algorithm' by Simplified Fixed Point Iteration in Adaptive Model Predictive Control

机译：关于自适应模型预测控制中的简化定点迭代替换拉格朗日的“降低梯度算法”

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The idea of "Model Predictive Control" (MPC) means a wide framework that contains numerous particular approaches. If it is tackled from the side of numerical realization over a discrete time grid ("horizon") , it normally applies "Nonlinear Programming" (NP) that, by the use of Lagrange’s "Reduced Gradient Method" (RGM), minimizes a cost function under various constraints. The cost function used to be a weighted sum of nonnegative differentiable terms that normally means a compromise between various, often contradictory requirements, while the constraints normally contain the dynamic model of the controlled system to express its limited abilities. The computational needs of the method strongly depend on the structure of the cost function and the model. In the case of a Moore-Penrose Pseudoinverse only the computation of the inverse of a single quadratic matrix is necessary. If only quadratic cost terms and "Linear Time-invariant" (LTI) dynamic models occur, we arrive at Kalman’s "Linear Quadratic Regulator" (LQR) that can utilize the special advantages of the Riccati equation. It was recently recognized that for a wide class of problems, in analogy with a novel solution of the inverse kinematic task for robots, the gradient of the "Auxiliary Function" (AF) of the problem can be directly driven to 0 by "Fixed Point Iteration" (FPI). However, it was found that in control problems just the calculation of the Jacobian means considerable programming and computational burden. To release it a recent solution was proposed for solving the inverse kinematic task by evading not only the inversion, but even the calculation of the Jacobian. In the present paper it is shown by the use of a nonlinear single degree of freedom paradigm that this simplification may be a viable route in solving "Adaptive Receding Horizon Control" (ARHC) problems.
机译：“模型预测控制”（MPC）的概念意味着包含许多特定方法的广泛框架。如果从离散时间网格（“水平”）上的数值实现方面解决问题，通常会应用“非线性编程”（NP），该方法通过使用拉格朗日的“降低梯度法”（RGM）来最大程度地降低成本在各种约束下的功能。成本函数曾经是非负可微名词的加权和，通常意味着各种需求之间的折衷，这些需求通常相互矛盾，而约束通常包含受控系统的动态模型以表达其有限的能力。该方法的计算需求在很大程度上取决于成本函数和模型的结构。对于Moore-Penrose伪逆，只需计算单个二次矩阵的逆即可。如果仅出现二次成本项和“线性时不变”（LTI）动态模型，我们将得出Kalman的“线性二次调节器”（LQR），它可以利用Riccati方程的特殊优势。最近认识到，对于各种各样的问题，类似于机器人逆运动学任务的新颖解决方案，可以通过“固定点”将问题的“辅助功能”（AF）的梯度直接驱动为0。迭代”（FPI）。但是，已经发现，在控制问题中，仅雅可比算术的计算就意味着相当大的编程和计算负担。为了释放它，提出了一种最新的解决方案，该解决方案不仅通过避开反演，而且还避开雅可比算术的计算，来解决反运动学任务。在本文中，通过使用非线性单自由度范式显示，这种简化可能是解决“自适应后视水平控制”（ARHC）问题的可行途径。

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