Recent advances in learning-based control leverage deep function approximators, such as neural networks, to model the evolution of controlled dynamical systems over time. However, the problem of learning a dynamics model and a stabilizing controller persists, since the synthesis of a stabilizing feedback law for known nonlinear systems is a difficult task, let alone for complex parametric representations that must be fit to data. To this end, we propose Control with Inherent Lyapunov Stability (CoILS), a method for jointly learning parametric representations of a nonlinear dynamics model and a stabilizing controller from data. To do this, our approach simultaneously learns a parametric Lyapunov function which intrinsically constrains the dynamics model to be stabilizable by the learned controller. In addition to the stabilizability of the learned dynamics guaranteed by our novel construction, we show that the learned controller stabilizes the true dynamics under certain assumptions on the fidelity of the learned dynamics. Finally, we demonstrate the efficacy of CoILS on a variety of simulated nonlinear dynamical systems.
翻译:近年来,基于学习的控制方法利用深度函数逼近器如神经网络,对控制动态系统在时间上的演化进行建模。但是,学习动态模型和稳定控制器的问题仍然存在,因为即使是对于已知的非线性系统,综合一个稳定的反馈控制很困难,更不用说是针对要根据数据拟合的复杂参数表示进行控制。为此,我们提出了内在李亚普诺夫稳定性控制方法(Control with Inherent Lyapunov Stability, CoILS),该方法可以联合学习非线性动态模型的参数表示和稳定控制器。为了实现这个目的,我们的方法同时学习参数李亚普诺夫函数,它在本质上将动态模型限定为可以被所学习的控制器稳定。除了利用我们的新方法保证已学习的动态模型的稳定性外,我们还展示了在学习的动态模型保真度方面的一些假设下,所学习的控制器可以稳定真实的动态系统。最后,我们在多个仿真非线性动态系统上展示了CoILS方法的有效性。