论文标题
在不确定性下的分布强劲的Lyapunov功能搜索
Distributionally Robust Lyapunov Function Search Under Uncertainty
论文作者
论文摘要
本文开发了证明动态系统的Lyapunov稳定性的方法，但受到不明分布的干扰。我们假设只有一组有限的干扰样本，并且可以从与给定样本不同的分布中得出真正的在线干扰实现。我们制定了一个优化问题，以搜索一个方格（SOS）lyapunov函数，并引入Lyapunov函数衍生限制的分布稳健版本。我们表明，该约束可能被重新重新定义为几个SOS约束，以确保对Lyapunov函数的搜索仍然存在于SOS多项式优化问题类别中。对于一般系统，我们为神经网络Lyapunov功能搜索提供了一个具有分布强大的机会约束的公式。模拟证明了两种公式在非线性不确定动力学系统上的有效性和效率。
This paper develops methods for proving Lyapunov stability of dynamical systems subject to disturbances with an unknown distribution. We assume only a finite set of disturbance samples is available and that the true online disturbance realization may be drawn from a different distribution than the given samples. We formulate an optimization problem to search for a sum-of-squares (SOS) Lyapunov function and introduce a distributionally robust version of the Lyapunov function derivative constraint. We show that this constraint may be reformulated as several SOS constraints, ensuring that the search for a Lyapunov function remains in the class of SOS polynomial optimization problems. For general systems, we provide a distributionally robust chance-constrained formulation for neural network Lyapunov function search. Simulations demonstrate the validity and efficiency of either formulation on non-linear uncertain dynamical systems.
