An efficient implementation of partial condensing for Nonlinear Model Predictive Control
An efficient implementation of partial condensing for Nonlinear Model Predictive Control
复制标题
非线性模型预测控制部分压缩的有效实现
DOI：
10.1109/cdc.2016.7798946
复制
发表时间：
2016
期刊：
影响因子：
--
通讯作者：
M. Diehl
中科院分区：
文献类型：
--
作者：
G. Frison;Dimitris Kouzoupis;J. B. Jørgensen;M. Diehl
部分（或块）冷凝是最近提出的一种技术，将模型预测控制（MPC）问题转化为更适合于结构开发二次规划（QP）求解器的形式。它权衡输入向量大小的水平长度，并且该自由度可以用于找到手头的QP求解器的最佳问题大小。本文提出了一种Hessian凝聚算法，特别适合于部分凝聚，其中一个状态分量被保留作为优化变量在每个阶段的部分凝聚MPC问题。从理论的角度（基于算法的触发器计数）以及基准测试（在实践中，不同矩阵大小的线性代数例程的性能起着关键作用）的最佳输入范围的权衡研究。部分压缩也可以被看作是一种技术，用更少的操作来代替对小矩阵的操作，其中线性代数例程执行得更好。因此，在小规模MPC问题的情况下，部分压缩可以大大提高性能，而不仅仅是减少触发器计数。
Partial (or block) condensing is a recently proposed technique to reformulate a Model Predictive Control (MPC) problem into a form more suitable for structure-exploiting Quadratic Programming (QP) solvers. It trades off horizon length for input vector size, and this degree of freedom can be employed to find the best problem size for the QP solver at hand. This paper proposes a Hessian condensing algorithm particularly well suited for partial condensing, where a state component is retained as an optimization variable at each stage of the partially condensed MPC problem. The optimal input-horizon trade-off is investigated from a theoretical point of view (based on algorithms flop count) as well as by benchmarking (in practice, the performance of linear algebra routines for different matrix sizes plays a key role). Partial condensing can also be seen as a technique to replace many operations on small matrices with fewer operations on larger matrices, where linear algebra routines perform better. Therefore, in case of small-scale MPC problems, partial condensing can greatly improve performance beyond the flop count reduction.