论文标题
基于库普曼的固定时间识别的未知非线性系统的安全控制设计
Safe Control Design for Unknown Nonlinear Systems with Koopman-based Fixed-Time Identification
论文作者
论文摘要
我们考虑一类未知，添加剂，非线性干扰的一类非线性，控制型系统的安全控制设计问题。利用Koopman运算符理论在系统识别和控制领域的应用中的最新进步，我们引入了一种新型的固定时间识别方案，用于无限二维的无限发电机，但尤其是线性的Koopman动力学系统类似于非线性感兴趣的系统。也就是说，我们得出了一种参数适应定律，该定律使我们能够在有限的时间内恢复系统中未知的残留非线性动力学，而独立于初始估计。然后，我们使用固定时间稳定性的属性来得出在残留矢量字段估计误差上绑定的错误作为时间的显式函数，这使我们能够使用基于控制屏障函数的方法合成可证明的安全控制器。我们进行了四型启发的案例研究，以支持我们提出的方法，其中我们表明，尽管未知的非线性动力学，但仍可以实现安全轨迹跟踪。
We consider the problem of safe control design for a class of nonlinear, control-affine systems subject to an unknown, additive, nonlinear disturbance. Leveraging recent advancements in the application of Koopman operator theory to the field of system identification and control, we introduce a novel fixed-time identification scheme for the infinitesimal generator of the infinite-dimensional, but notably linear, Koopman dynamical system analogous to the nonlinear system of interest. That is, we derive a parameter adaptation law that allows us to recover the unknown, residual nonlinear dynamics in the system within a finite-time independent of an initial estimate. We then use properties of fixed-time stability to derive an error bound on the residual vector field estimation error as an explicit function of time, which allows us to synthesize a provably safe controller using control barrier function based methods. We conduct a quadrotor-inspired case study in support of our proposed method, in which we show that safe trajectory tracking is achieved despite unknown, nonlinear dynamics.
