Quadrature-based scenario tree generation for Nonlinear Model Predictive Control
Quadrature-based scenario tree generation for Nonlinear Model Predictive Control
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DOI：
10.3182/20140824-6-za-1003.02535
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
Conrad Leidereiter;A. Potschka;H. Bock
中科院分区：
文献类型：
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作者：
Conrad Leidereiter;A. Potschka;H. Bock
摘要一种较新的鲁棒非线性模型预测控制（NMPC）方法是基于情景树和一个所谓的追索公式。这种方法很有趣，因为它比最坏情况的鲁棒方法保守性更低。使用场景树进行鲁棒NMPC时的一个主要挑战是大量的场景，这些场景呈指数级增长。这种指数增长很快成为计算成本的瓶颈，需要保持在允许实时适用性的范围内。我们提出了如何生成场景的基础上求积规则的期望值的任意经济目标函数。使用稀疏网格的高维随机积分的求积产生了一个显着更少的情况下比张量网格方法使用至今。我们比较了几个强大的NMPC方法的性能为三个正态分布的不确定性参数的精馏塔内的模拟蒙特-卡罗控制器测试平台。
Abstract A relatively recent approach for robust Nonlinear Model Predictive Control (NMPC) is based on scenario trees with a so-called recourse formulation. This approach is of interest, because it is less conservative than worst-case robustification approaches. A major challenge when using scenario trees for robust NMPC is the large number of scenarios, which grows exponentially. This exponential growth quickly becomes a bottleneck for the computational costs, which need to stay within bounds that permit real-time applicability. We present how to generate scenarios based on a quadrature rule for the expectation value of an arbitrary economic objective function. The use of sparse grids for the quadrature of the high-dimensional stochastic integrals yields a drastically smaller number of scenarios than the tensor grid approaches used so far. We compare the performance of several robust NMPC approaches for a distillation column with three normally distributed uncertain parameters within a simulated Monte-Carlo controller testbed.