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Introducing System Identification Strategy into Model Predictive Control
Journal of Systems Science and Complexity ( IF 2.6 ) Pub Date : 2020-10-08 , DOI: 10.1007/s11424-020-9058-3
Jianhong Wang , A. Ramirez-Mendoza Ricardo , de J Lozoya Santos Jorge

As system identification theory and model predictive control are belonged to two different research fields separately, so one gap exists between these two subjects. To alleviate this gap between them, one new idea proposed in this paper is to introduce system identification theory into model predictive control. As the most important element in model predictive control is the prediction of the output value for a nonlinear system, then the problem of deriving the prediction of the output value can be achieved by system identification theory. More specifically, a Bayesian approach is applied for the nonparametric estimation by modeling the prediction as realizations of zero mean random fields. Through comparing this kind of prediction corresponding to this Bayesian approach and the former direct weight optimization identification for nonlinear system, the authors see that if the unknown weights are chosen appropriately, these two approaches are equivalent to each other. Based on the obtained prediction of the output value, the authors substitute this prediction of the output value into one cost function of model predictive control, and then a quadratic programming problem with inequality constraints is formulated. When to solve this quadratic programming problem, a detailed process about how to derive its dual form is given. As the dual problem has a simple constraint set, it is amenable to the use of the common Gauss-Seidel algorithm, whose convergence can be shown easily. Finally, one simulation example confirms the proposed theoretical results.



中文翻译:

将系统识别策略引入模型预测控制

由于系统识别理论和模型预测控制分别属于两个不同的研究领域,因此这两个主题之间存在一个空白。为了减轻它们之间的差距,本文提出的一个新想法是将系统识别理论引入模型预测控制中。由于模型预测控制中最重要的元素是非线性系统的输出值预测,因此可以通过系统识别理论来解决推导输出值预测的问题。更具体地,通过将​​预测建模为零平均随机场的实现,将贝叶斯方法应用于非参数估计。通过比较与这种贝叶斯方法相对应的这种预测和非线性系统以前的直接权重优化识别,作者发现,如果适当地选择未知权重,则这两种方法彼此等效。基于获得的输出值预测,作者将这一输出值预测代入模型预测控制的一个成本函数,然后提出了一个具有不等式约束的二次规划问题。当解决该二次编程问题时,给出了有关如何导出其对偶形式的详细过程。由于对偶问题具有简单的约束集,因此可以使用常见的Gauss-Seidel算法,该算法的收敛性易于显示。最后,一个仿真例子证实了所提出的理论结果。基于获得的输出值预测,作者将这一输出值预测代入模型预测控制的一个成本函数,然后提出了一个具有不等式约束的二次规划问题。当解决该二次编程问题时,给出了有关如何导出其对偶形式的详细过程。由于对偶问题具有简单的约束集,因此可以使用常见的Gauss-Seidel算法,该算法的收敛性易于显示。最后,一个仿真例子证实了所提出的理论结果。基于获得的输出值预测,作者将这一输出值预测代入模型预测控制的一个成本函数,然后提出了一个具有不等式约束的二次规划问题。当解决该二次编程问题时,给出了有关如何导出其对偶形式的详细过程。由于对偶问题具有简单的约束集,因此可以使用常见的Gauss-Seidel算法,该算法的收敛性易于显示。最后,一个仿真例子证实了所提出的理论结果。给出了有关如何导出其对偶形式的详细过程。由于对偶问题具有简单的约束集,因此可以使用常见的Gauss-Seidel算法,该算法的收敛性易于显示。最后,一个仿真例子证实了所提出的理论结果。给出了有关如何导出其对偶形式的详细过程。由于对偶问题具有简单的约束集,因此可以使用常见的Gauss-Seidel算法,该算法的收敛性易于显示。最后,一个仿真例子证实了所提出的理论结果。

更新日期:2020-10-30
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