论文标题
线性预测控制的无关的预处理设计
Horizon-independent Preconditioner Design for Linear Predictive Control
论文作者
论文摘要
一阶优化求解器（例如快速梯度方法）越来越多地用于解决资源受限环境中的模型预测控制问题。不幸的是，这些求解器的收敛速率受到问题数据的条件的显着影响，条件不足的问题需要大量迭代。为了减少所需的迭代次数，我们提出了一种简单的方法，用于计算凝结问题的黑森的无关预处理矩阵。预处理基于Hessian的块Toeplitz结构。 Horizon Intepentions允许仅使用预测的系统和成本矩阵来计算预处理，而不是完整的Hessian。所提出的预处理在数值示例中具有等效性能与最佳预处理的性能，对于快速梯度方法产生了2倍至9倍的加速度。此外，我们根据预测系统的传递函数得出了黑森的无关光谱界限，并显示如何用于计算预处理的Hessian的条件号上的新型地平线独立结合。
First-order optimization solvers, such as the Fast Gradient Method, are increasingly being used to solve Model Predictive Control problems in resource-constrained environments. Unfortunately, the convergence rate of these solvers is significantly affected by the conditioning of the problem data, with ill-conditioned problems requiring a large number of iterations. To reduce the number of iterations required, we present a simple method for computing a horizon-independent preconditioning matrix for the Hessian of the condensed problem. The preconditioner is based on the block Toeplitz structure of the Hessian. Horizon-independence allows one to use only the predicted system and cost matrices to compute the preconditioner, instead of the full Hessian. The proposed preconditioner has equivalent performance to an optimal preconditioner in numerical examples, producing speedups between 2x and 9x for the Fast Gradient Method. Additionally, we derive horizon-independent spectral bounds for the Hessian in terms of the transfer function of the predicted system, and show how these can be used to compute a novel horizon-independent bound on the condition number for the preconditioned Hessian.
