论文标题
通过在线检测州空间集加速MPC，并具有常见的最佳反馈法律
Accelerating MPC by online detection of state space sets with common optimal feedback laws
论文作者
论文摘要
模型预测控制（MPC）逐点采样了一个通常未知和复杂的反馈定律。但是，当前状态$ x $的解决方案包含更多的信息，而不是该特定状态的最佳信号$ u $。实际上，它在polytope $π\ subset \ mathbb {r}^n $，即在全维状态空间集上提供了最佳的仿射反馈定律$ x \ rightarrow u（x）$。尽可能长时间重复此仿射反馈法是一个明显的想法。但是，在其polytope $π$上重复使用它是太保守了，因为任何$π$都是具有通用仿射定律$ x \ rightarrow（u_0^\ prime（x），\ dots，u_ {n-1}^\ prime（x）^prime \ prime \ in \ mathbb in \ mathbb {r r} $ n，我们显示了一个简单的标准，用于识别具有共同的$ x \ rightarrow u_0（x）$的多型，但在$ u_1（x），\ dots，u_ {n-1}（x）$方面可能有所不同。由于此标准在在线使用上太昂贵了，因此我们引入了一种简单的启发式方法，以快速构建感兴趣的多型的子集。计算示例表明（i）可以避免QP的相当一部分（10％至40％），并且（ii）启发式方法导致如果有明确的解决方案，可以使降低非常接近最大值。我们强调提出的方法旨在用于在线MPC，并且不需要明确的解决方案。
Model predictive control (MPC) samples a generally unknown and complicated feedback law point by point. The solution for the current state $x$ contains, however, more information than only the optimal signal $u$ for this particular state. In fact, it provides an optimal affine feedback law $x\rightarrow u(x)$ on a polytope $Π\subset \mathbb{R}^n$, i.e., on a full-dimensional state space set. It is an obvious idea to reuse this affine feedback law as long as possible. Reusing it on its polytope $Π$ is too conservative, however, because any $Π$ is a state space set with a common affine law $x\rightarrow (u_0^\prime (x), \dots, u_{N-1}^\prime (x))^\prime\in\mathbb{R}^{Nm}$ for the entire horizon $N$. We show a simple criterion exists for identifying the polytopes that have a common $x\rightarrow u_0(x)$, but may differ with respect to $u_1(x), \dots, u_{N-1}(x)$. Because this criterion is too computationally expensive for an online use, we introduce a simple heuristics for the fast construction of a subset of the polytopes of interest. Computational examples show (i) a considerable fraction of QPs can be avoided (10% to 40%) and (ii) the heuristics results in a reduction very close to the maximum one that could be achieved if the explicit solution was available. We stress the proposed approach is intended for use in online MPC and it does not require the explicit solution.
