论文标题
来自嘈杂数据的线性二次调节器的低复杂性学习
Low-complexity Learning of Linear Quadratic Regulators from Noisy Data
论文作者
论文摘要
本文考虑了具有未知动力学的线性系统的线性二次调节器问题，这是数据驱动控制和增强学习中的核心问题。我们提出了一种使用数据直接返回控制器的方法，而无需估计系统模型。给出了足够的条件，该方法在该方法返回稳定控制器的情况下，当用于设计控制器的数据受噪声影响时，具有保证的相对误差。此方法的复杂性很低，因为它仅需要系统响应的有限数量对足够令人兴奋的输入的响应，并且可以有效地作为半明确程序实现。此外，该方法不需要关于噪声统计数据的假设，并且相对误差与噪声幅度很好地缩放。
This paper considers the Linear Quadratic Regulator problem for linear systems with unknown dynamics, a central problem in data-driven control and reinforcement learning. We propose a method that uses data to directly return a controller without estimating a model of the system. Sufficient conditions are given under which this method returns a stabilizing controller with guaranteed relative error when the data used to design the controller are affected by noise. This method has low complexity as it only requires a finite number of samples of the system response to a sufficiently exciting input, and can be efficiently implemented as a semi-definite program. Further, the method does not require assumptions on the noise statistics, and the relative error nicely scales with the noise magnitude.
