论文标题
神经Koopman控制障碍功能，用于对未知非线性系统的安全关键控制
Neural Koopman Control Barrier Functions for Safety-Critical Control of Unknown Nonlinear Systems
论文作者
论文摘要
我们考虑使用控制屏障功能（CBF）的非线性系统合成安全控制器的问题。我们利用Koopman操作员理论（KOT）将（未知）的非线性系统与更高的双线性系统相关联，并提出了一个数据驱动的学习框架，该框架使用学习者和虚假者同时学习基于Koopman操作员的双线性双线性系统和相应的CBF。我们证明，通过表征这两个系统之间绑定的$ \ ell^2 $ -Norm误差，通过表征$ \ ell^2 $ -Norm误差，对后者双线性系统的学习CBF也是对未知非线性系统的有效CBF。我们表明，可以使用基于Koopman的可观测值的Lipschitz常数来部分调整此误差。然后，CBF用于制定二次程序，以计算保证未知非线性系统安全的输入。提出数值模拟以验证我们的方法。
We consider the problem of synthesis of safe controllers for nonlinear systems with unknown dynamics using Control Barrier Functions (CBF). We utilize Koopman operator theory (KOT) to associate the (unknown) nonlinear system with a higher dimensional bilinear system and propose a data-driven learning framework that uses a learner and a falsifier to simultaneously learn the Koopman operator based bilinear system and a corresponding CBF. We prove that the learned CBF for the latter bilinear system is also a valid CBF for the unknown nonlinear system by characterizing the $\ell^2$-norm error bound between these two systems. We show that this error can be partially tuned by using the Lipschitz constant of the Koopman based observables. The CBF is then used to formulate a quadratic program to compute inputs that guarantee safety of the unknown nonlinear system. Numerical simulations are presented to validate our approach.
