We present a new deep learning-based adaptive control framework for nonlinear systems with multiplicatively-separable parametric uncertainty, called an adaptive Neural Contraction Metric (aNCM). The aNCM uses a neural network model of an optimal adaptive contraction metric, the existence of which guarantees asymptotic stability and exponential boundedness of system trajectories under the parametric uncertainty. In particular, we exploit the concept of a Neural Contraction Metric (NCM) to obtain a nominal provably stable robust control policy for nonlinear systems with bounded disturbances, and combine this policy with a novel adaptation law to achieve stability guarantees. We also show that the framework is applicable to adaptive control of dynamical systems modeled via basis function approximation. Furthermore, the use of neural networks in the aNCM permits its real-time implementation, resulting in broad applicability to a variety of systems. Its superiority to the state-of-the-art is illustrated with a simple cart-pole balancing task.

中文翻译：

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收缩理论的基于学习的自适应控制

我们为非线性系统提供了一种基于深度学习的新的自适应控制框架，该系统具有可乘性分离的参数不确定性，称为自适应神经收缩度量（aNCM）。aNCM使用最佳自适应收缩度量的神经网络模型，该模型的存在保证了在参数不确定性下系统轨迹的渐近稳定性和指数有界性。尤其是，我们利用神经收缩度量（NCM）的概念来获得具有有限扰动的非线性系统的名义上可证明的稳定鲁棒控制策略，并将该策略与新颖的自适应律相结合以实现稳定性保证。我们还表明，该框架适用于通过基函数逼近建模的动态系统的自适应控制。此外，在aNCM中使用神经网络可以实现其实时实施，从而广泛适用于各种系统。一个简单的平衡杆任务说明了它在最新技术方面的优越性。