论文标题
积极学习以识别线性动力学系统
Active Learning for Identification of Linear Dynamical Systems
论文作者
论文摘要
我们提出了一种算法来积极估计线性动力学系统的参数。鉴于对系统输入的完全控制，我们的算法自适应地选择了输入以加速估计。我们显示了有限的时间结合，量化了我们的算法达到的估计率，并证明了匹配的上限和下限，从而确保其渐近最佳性，直到常数。此外，我们表明，即使使用高斯噪声来激发系统，即使使用最佳调节协方差，这种最佳速率是无法实现的，并分析了几个示例，在这些示例中，我们的算法可证明通过播放噪声来提高速率超过速率。我们的分析非常依赖于新的结果，该结果量化了在播放任意周期性输入时估计动态系统参数时的误差。我们以数值示例结束，这些示例说明了我们算法在实践中的有效性。
We propose an algorithm to actively estimate the parameters of a linear dynamical system. Given complete control over the system's input, our algorithm adaptively chooses the inputs to accelerate estimation. We show a finite time bound quantifying the estimation rate our algorithm attains and prove matching upper and lower bounds which guarantee its asymptotic optimality, up to constants. In addition, we show that this optimal rate is unattainable when using Gaussian noise to excite the system, even with optimally tuned covariance, and analyze several examples where our algorithm provably improves over rates obtained by playing noise. Our analysis critically relies on a novel result quantifying the error in estimating the parameters of a dynamical system when arbitrary periodic inputs are being played. We conclude with numerical examples that illustrate the effectiveness of our algorithm in practice.
