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 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 our method on a variety of simulated nonlinear dynamical systems.

翻译：近期基于学习的控制领域进展，利用深度函数逼近器（如神经网络）对受控动力系统的时间演化过程进行建模。然而，学习动力学模型与稳定控制器的问题依然存在，因为即使对于已知非线性系统，综合稳定反馈律本身就是一项艰巨任务，更遑论必须通过数据拟合的复杂参数化表示。为此，我们提出一种从数据中联合学习非线性动力学模型与稳定控制器的参数化表示方法。该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被所学习的控制器稳定。除了通过新颖构造保证所学动力学的可稳性外，我们进一步证明：在所学动力学保真度的特定假设条件下，该控制器能稳定真实动力学系统。最后，我们通过多种模拟非线性动力系统验证了该方法的有效性。