模型预测控制中Riccati分解的低阶修正
Low-Rank Modifications of Riccati Factorizations for Model Predictive Control
摘要：
在模型预测控制（MPC）中，通过在控制回路中的每个样本处求解受限有限时间最优控制（CFTOC）问题来计算控制输入。主要的计算工作通常花费在计算搜索方向上，这在MPC中对应于求解无约束有限时间最优控制（UFTOC）问题。这通常使用Riccati递归或通用稀疏性利用算法来执行。在这项工作中，重点是有效的搜索方向计算活跃集（AS）类型的方法。在每次AS迭代中要求解的方程组仅通过对前一次的低秩修改来改变，并且利用这种结构变化对于AS型求解器的性能是重要的。在本文中，理论如何利用这些低秩的变化，通过修改的Riccati分解AS迭代之间的结构化的方式。所提出的算法的数值评估表明，计算时间可以显着减少修改，而不是重新计算，Riccati分解。这种加速对于用于线性、非线性和混合MPC的AS型解算器可能是重要的。
英文摘要：
In Model Predictive Control (MPC) the control input is computed by solving a constrained finite-time optimal control (CFTOC) problem at each sample in the control loop. The main computational effort is often spent on computing the search directions, which in MPC corresponds to solving unconstrained finite-time optimal control (UFTOC) problems. This is commonly performed using Riccati recursions or generic sparsity exploiting algorithms. In this work the focus is efficient search direction computations for active-set (AS) type methods. The system of equations to be solved at each AS iteration is changed only by a low-rank modification of the previous one, and exploiting this structured change is important for the performance of AS type solvers. In this paper, theory for how to exploit these low-rank changes by modifying the Riccati factorization between AS iterations in a structured way is presented. A numerical evaluation of the proposed algorithm shows that the computation time can be significantly reduced by modifying, instead of re-computing, the Riccati factorization. This speed-up can be important for AS type solvers used for linear, nonlinear and hybrid MPC.
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