Memory-Efficient Learning of Stable Linear Dynamical Systems for Prediction and Control
Memory-Efficient Learning of Stable Linear Dynamical Systems for Prediction and Control
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发表时间：
2020-06
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通讯作者：
Giorgos Mamakoukas;Orest Xherija;T. Murphey
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作者：
Giorgos Mamakoukas;Orest Xherija;T. Murphey
从数据中学习稳定的线性动态系统（LDS）涉及创建模型，这些模型既可以最大限度地减少重建误差，又可以加强学习表示的稳定性。我们提出了一种新的算法学习稳定的LDS。使用最近的稳定矩阵的表征，我们提出了一种优化方法，确保在每一步的稳定性，并迭代地提高重建误差使用本文导出的梯度方向。当应用于LDSs的输入，我们的方法-在目前的方法学习稳定的LDSs-更新的状态和控制矩阵，扩大解决方案的空间，并允许模型具有较低的重建误差。我们将我们的算法在模拟和实验中应用到各种问题，包括从图像序列中学习动态纹理和控制机器人操纵器。与现有的方法相比，我们提出的方法实现了数量级的改善重建误差和上级的控制性能方面的结果。此外，它被证明是更高效的内存，与竞争的替代方案相比，空间复杂度为O（n^2），因此当其他方法失败时，可以扩展到更高维的系统。
Learning a stable Linear Dynamical System (LDS) from data involves creating models that both minimize reconstruction error and enforce stability of the learned representation. We propose a novel algorithm for learning stable LDSs. Using a recent characterization of stable matrices, we present an optimization method that ensures stability at every step and iteratively improves the reconstruction error using gradient directions derived in this paper. When applied to LDSs with inputs, our approach---in contrast to current methods for learning stable LDSs---updates both the state and control matrices, expanding the solution space and allowing for models with lower reconstruction error. We apply our algorithm in simulations and experiments to a variety of problems, including learning dynamic textures from image sequences and controlling a robotic manipulator. Compared to existing approaches, our proposed method achieves an orders-of-magnitude improvement in reconstruction error and superior results in terms of control performance. In addition, it is provably more memory-efficient, with an O(n^2) space complexity compared to O(n^4) of competing alternatives, thus scaling to higher-dimensional systems when the other methods fail.