论文标题
方案总和计划和安全学习，以最大化部分未知系统的吸引力区域
Sum-of-Squares Program and Safe Learning On Maximizing the Region of Attraction of Partially Unknown Systems
论文作者
论文摘要
最新的学习技术进步使直接从数据直接从数据建模。但是，在许多情况下，这些基于学习的方法缺乏安全保证和严格的稳定性验证。为了解决这个问题，本文首先使用具有高斯流程和Chebyshev插值的学习状态空间来近似部分未知的非线性系统。然后，提出了基于平方的计划的方法，以通过搜索最佳控制Lyapunov屏障函数来综合控制器。这样，我们最大程度地提高了部分未知的非线性系统的吸引力区域，同时确保安全性和稳定性。结果表明，所提出的方法改善了外推性能，同时会产生更大的估计吸引区域。
Recent advances in learning techniques have enabled the modelling of unknown dynamical systems directly from data. However, in many contexts, these learning-based methods are short of safety guarantee and strict stability verification. To address this issue, this paper first approximates the partially unknown nonlinear systems by using a learned state space with Gaussian Processes and Chebyshev interpolants. A Sum-of-Squares Programming based approach is then proposed to synthesize a controller by searching an optimal control Lyapunov Barrier function. In this way, we maximize the estimated region of attraction of partially unknown nonlinear systems, while guaranteeing both safety and stability. It is shown that the proposed method improves the extrapolation performance, and at the same time, generates a significantly larger estimated region of attraction.
