This work focuses on developing a data-driven framework using Koopman
operator theory for system identification and linearization of nonlinear
systems for control. Our proposed method presents a deep learning framework
with recursive learning. The resulting linear system is controlled using a
linear quadratic control. An illustrative example using a pendulum system is
presented with simulations on noisy data. We show that our proposed method is
trained more efficiently and is more accurate than an autoencoder baseline.

使用 Koopman 算子理论开发了一个基于数据驱动的框架，用于非线性系统的系统识别和线性化控制，采用递归学习的深度学习框架，并使用线性二次控制器对得到的线性系统进行控制。通过在噪声数据上进行仿真，我们展示了我们的方法相比自编码器基准更高效且更准确的训练结果。

非线性系统的计算高效数据驱动发现与线性表示

Computationally Efficient Data-Driven Discovery and Linear  Representation of Nonlinear Systems For Control

This paper considers a distributed reinforcement learning problem for
decentralized linear quadratic control with partial state observations and
local costs. We propose a Zero-Order Distributed Policy Optimization algorithm
(ZODPO) that learns linear local controllers in a distributed fashion,
leveraging the ideas of policy gradient, zero-order optimization and consensus
algorithms. In ZODPO, each agent estimates the global cost by consensus, and
then conducts local policy gradient in parallel based on zero-order gradient
estimation. ZODPO only requires limited communication and storage even in
large-scale systems. Further, we investigate the nonasymptotic performance of
ZODPO and show that the sample complexity to approach a stationary point is
polynomial with the error tolerance's inverse and the problem dimensions,
demonstrating the scalability of ZODPO. We also show that the controllers
generated throughout ZODPO are stabilizing controllers with high probability.
Lastly, we numerically test ZODPO on multi-zone HVAC systems.

本文提出了一种名为 ZODPO 的算法，它是一种基于 policy gradient、零阶优化和共识算法的分布式强化学习算法，用于解决分散线性二次控制问题，该算法具有良好的可伸缩性，适用于大规模系统，并可用于多区域 HVAC 系统。

分布式强化学习应用于分布式线性二次控制：无导数策略优化方法

Distributed Reinforcement Learning for Decentralized Linear Quadratic  Control: A Derivative-Free Policy Optimization Approach

We study the performance of the certainty equivalent controller on Linear
Quadratic (LQ) control problems with unknown transition dynamics. We show that
for both the fully and partially observed settings, the sub-optimality gap
between the cost incurred by playing the certainty equivalent controller on the
true system and the cost incurred by using the optimal LQ controller enjoys a
fast statistical rate, scaling as the square of the parameter error. To the
best of our knowledge, our result is the first sub-optimality guarantee in the
partially observed Linear Quadratic Gaussian (LQG) setting. Furthermore, in the
fully observed Linear Quadratic Regulator (LQR), our result improves upon
recent work by Dean et al. (2017), who present an algorithm achieving a
sub-optimality gap linear in the parameter error. A key part of our analysis
relies on perturbation bounds for discrete Riccati equations. We provide two
new perturbation bounds, one that expands on an existing result from
Konstantinov et al. (1993), and another based on a new elementary proof
strategy.

研究了采用确定性等价控制器处理具有未知传递动态的线性二次（LQ）控制问题的性能。通过使用摸不清全监控和部分监控下的确定性等价控制器处理真实系统和使用最优 LQ 控制器之间的成本，我们证明了在参数误差的平方速率下的亚最优差。我们提供了两个新的微扰界限，其中一个扩展了 Konstantinov 等人（1993）的现有结果，另一个基于新的初等证明策略。