论文标题
可证明对线性动力学的学习稳定学习控制，并具有乘法噪声
Provably stable learning control of linear dynamics with multiplicative noise
论文作者
论文摘要
用乘法噪声控制线性动力学自然会引入动力学不确定性的鲁棒性。此外，许多物理系统都会受到乘法干扰。在这项工作中，我们展示了如何从状态轨迹中识别这些动态。最小二乘方案可以利用先前的信息，并带有实际数据驱动的置信界和样本复杂性保证。我们将该方案与LQR相关的控制综合程序进行补充，该过程可鲁棒地抵抗分布不确定性，以高概率确保稳定性，并以与样品计数成反比的速率收敛到真实最佳。在整个过程中，我们通过张量代数和完全积极的运算符来利用潜在的多线性问题结构。该方案通过数值实验验证。
Control of linear dynamics with multiplicative noise naturally introduces robustness against dynamical uncertainty. Moreover, many physical systems are subject to multiplicative disturbances. In this work we show how these dynamics can be identified from state trajectories. The least-squares scheme enables exploitation of prior information and comes with practical data-driven confidence bounds and sample complexity guarantees. We complement this scheme with an associated control synthesis procedure for LQR which robustifies against distributional uncertainty, guaranteeing stability with high probability and converging to the true optimum at a rate inversely proportional with the sample count. Throughout we exploit the underlying multi-linear problem structure through tensor algebra and completely positive operators. The scheme is validated through numerical experiments.
