We consider the problem of designing a machine learning-based model of an
unknown dynamical system from a finite number of (state-input)-successor state
data points, such that the model obtained is also suitable for optimal control
design. We propose a specific neural network (NN) architecture that yields a
hybrid system with piecewise-affine dynamics that is differentiable with
respect to the network's parameters, thereby enabling the use of
derivative-based training procedures. We show that a careful choice of our NN's
weights produces a hybrid system model with structural properties that are
highly favourable when used as part of a finite horizon optimal control problem
(OCP). Specifically, we show that optimal solutions with strong local
optimality guarantees can be computed via nonlinear programming, in contrast to
classical OCPs for general hybrid systems which typically require mixed-integer
optimization. In addition to being well-suited for optimal control design,
numerical simulations illustrate that our NN-based technique enjoys very
similar performance to state-of-the-art system identification methodologies for
hybrid systems and it is competitive on nonlinear benchmarks.

我们考虑从有限数量的（状态 - 输入）- 后继状态数据点中设计一种基于机器学习的未知动态系统模型的问题，以便获得的模型也适用于最优控制设计。我们提出了一种特定的神经网络（NN）结构，其产生具有分段仿射动力学的混合系统，对网络参数具有可微性，从而使得能够使用基于导数的训练过程。我们展示了对 NN 权重的精心选择产生具有结构特性的混合系统模型，在有限视野最优控制问题（OCP）的计算方面具有非常有利条件。具体而言，我们表明可以通过非线性规划计算具有强大局部最优性保证的最优解，与通常需要混合整数优化的一般混合系统的经典 OCP 相比。除了非常适用于最优控制设计外，数值模拟还说明我们基于 NN 的技术在混合系统的系统识别方法方面具有非常类似的性能，并且在非线性基准测试中具有竞争力。

基于神经网络的混合系统辨识方法

A neural network-based approach to hybrid systems identification for  control

With the rapid increase in the number of Anthropogenic Space Objects (ASOs),
Low Earth Orbit (LEO) is facing significant congestion, thereby posing
challenges to space operators and risking the viability of the space
environment for varied uses. Current models for examining this evolution, while
detailed, are computationally demanding. To address these issues, we propose a
novel machine learning-based model, as an extension of the MIT Orbital Capacity
Tool (MOCAT). This advanced model is designed to accelerate the propagation of
ASO density distributions, and it is trained on hundreds of simulations
generated by an established and accurate model of the space environment
evolution. We study how different deep learning-based solutions can potentially
be good candidates for ASO propagation and manage the high-dimensionality of
the data. To assess the model's capabilities, we conduct experiments in long
term forecasting scenarios (around 100 years), analyze how and why the
performance degrades over time, and discuss potential solutions to make this
solution better.

提出了一种机器学习模型以加速人工空间目标的密度分布的传播，并通过长期预测实验来评估模型的能力和性能退化原因及解决方案。