Model predictive control (MPC) for linear systems with quadratic costs and
linear constraints is shown to admit an exact representation as an implicit
neural network. A method to "unravel" the implicit neural network of MPC into
an explicit one is also introduced. As well as building links between
model-based and data-driven control, these results emphasize the capability of
implicit neural networks for representing solutions of optimisation problems,
as such problems are themselves implicitly defined functions.

用隐式神经网络准确表示具有二次成本和线性约束的线性系统的模型预测控制，并引入一种将隐式神经网络解开为显式网络的方法，这些结果强调了隐式神经网络表示优化问题解决方案的能力，因为这些问题本身是隐式定义的函数。

模型预测控制与神经网络之间的映射

Mapping back and forth between model predictive control and neural  networks

In this paper, we study the problem of online tracking in linear control
systems, where the objective is to follow a moving target. Unlike classical
tracking control, the target is unknown, non-stationary, and its state is
revealed sequentially, thus, fitting the framework of online non-stochastic
control. We consider the case of quadratic costs and propose a new algorithm,
called predictive linear online tracking (PLOT). The algorithm uses recursive
least squares with exponential forgetting to learn a time-varying dynamic model
of the target. The learned model is used in the optimal policy under the
framework of receding horizon control. We show the dynamic regret of PLOT
scales with $\mathcal{O}(\sqrt{TV_T})$, where $V_T$ is the total variation of
the target dynamics and $T$ is the time horizon. Unlike prior work, our
theoretical results hold for non-stationary targets. We implement PLOT on a
real quadrotor and provide open-source software, thus, showcasing one of the
first successful applications of online control methods on real hardware.

研究在线跟踪线性控制系统中的问题，目标是追踪一个移动目标，提出了一种新的算法 PLOT，该算法使用递归最小二乘法和指数遗忘来学习目标的时变动态模型，并在前向视界控制框架下使用学到的模型。展示了 PLOT 的动态遗憾量与目标动力学的总变化量成正比，理论结果适用于非平稳目标，并在真实四旋翼上实施 PLOT，提供了开源软件，因此展示了在线控制方法在真实硬件上的成功应用之一。

未知目标的预测线性在线跟踪

Predictive Linear Online Tracking for Unknown Targets

A simple procedure to map two probability measures in $\mathbb{R}^d$ is the
so-called \emph{Knothe-Rosenblatt rearrangement}, which consists in rearranging
monotonically the marginal distributions of the last coordinate, and then the
conditional distributions, iteratively. We show that this mapping is the limit
of solutions to a class of Monge-Kantorovich mass transportation problems with
quadratic costs, with the weights of the coordinates asymptotically dominating
one another. This enables us to design a continuation method for numerically
solving the optimal transport problem.

本文介绍了一种基于 Knothe-Rosenblatt 置换的转换方法，该方法可用于解决具有二次代价的 Monge-Kantorovich 质量输运问题，详细介绍了优化输运问题的数值解法。