Efficient implementation of the Riccati recursion for solving linear-quadratic control problems

G. Frison, J. B. Jørgensen
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引用次数: 51

Abstract

In both Active-Set (AS) and Interior-Point (IP) algorithms for Model Predictive Control (MPC), sub-problems in the form of linear-quadratic (LQ) control problems need to be solved at each iteration. The solution of these sub-problems is typically the main computational effort at each iteration. In this paper, we compare a number of solvers for an extended formulation of the LQ control problem: a Riccati recursion based solver can be considered the best choice for the general problem with dense matrices. Furthermore, we present a novel version of the Riccati solver, that makes use of the Cholesky factorization of the Pn matrices to reduce the number of flops. When combined with regularization and mixed precision, this algorithm can solve large instances of the LQ control problem up to 3 times faster than the classical Riccati solver.
求解线性二次控制问题的Riccati递归的有效实现
在模型预测控制(MPC)的主动集(AS)和内点(IP)算法中,每次迭代都需要求解线性二次(LQ)控制问题的子问题。这些子问题的解决通常是每次迭代的主要计算工作。在本文中,我们比较了LQ控制问题的一个扩展公式的若干求解方法:对于具有密集矩阵的一般问题,基于Riccati递归的求解方法可以被认为是最佳选择。此外,我们提出了一个新版本的Riccati求解器,它利用Pn矩阵的Cholesky分解来减少flops的数量。当将正则化和混合精度相结合时,该算法可以解决LQ控制问题的大实例,比经典的Riccati求解器快3倍。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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