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：近期基于学习的控制进展利用深度函数近似器（如神经网络）对受控动力系统随时间演化的过程进行建模。然而，学习动力学模型与稳定控制器的问题仍然存在，这是因为即使对于已知的非线性系统，稳定反馈律的综合本身就是一项艰巨任务，更遑论需要从数据中拟合的复杂参数化表示。为此，我们提出"具有固有李雅普诺夫稳定性的控制方法"（CoILS），这是一种从数据中联合学习非线性动力学模型参数化表示及其稳定控制器的方法。我们的方法通过同步学习参数化李雅普诺夫函数，从本质上约束动力学模型必须能够被所学习的控制器稳定。除了通过这种新颖构造保证学习动力学的可稳定性外，我们还表明：在关于学习动力学精度的特定假设下，该控制器能够稳定真实动力学系统。最后，我们在多种仿真非线性动力学系统上验证了CoILS的有效性。