Adaptive control is subject to stability and performance issues when a learned model is used to enhance its performance. This paper thus presents a deep learning-based adaptive control framework for nonlinear systems with multiplicatively-separable parametrization, called adaptive Neural Contraction Metric (aNCM). The aNCM approximates real-time optimization for computing a differential Lyapunov function and a corresponding stabilizing adaptive control law by using a Deep Neural Network (DNN). The use of DNNs permits real-time implementation of the control law and broad applicability to a variety of nonlinear systems with parametric and nonparametric uncertainties. We show using contraction theory that the aNCM ensures exponential boundedness of the distance between the target and controlled trajectories in the presence of parametric uncertainties of the model, learning errors caused by aNCM approximation, and external disturbances. Its superiority to the existing robust and adaptive control methods is demonstrated using a cart-pole balancing model.
翻译:在使用一个学习模型来提高其性能时,适应性控制取决于稳定性和性能问题;因此,本文件为非线性系统提供了一个深层次的基于学习的适应性控制框架,称为适应性神经收缩仪(ANCM)。ANCM近似实时优化,用于计算不同的Lyapunov功能和相应的稳定性适应性控制法,使用深神经网络(DNN);DNN的使用允许实时执行控制法,并广泛适用于具有参数和非参数不确定性的各种非线性系统。我们用收缩理论表明,在模型存在参数不确定性、NCM近似引起的学习错误和外部扰动的情况下,ANCM确保目标与受控轨迹之间的距离的指数界限。它优于现有稳健和适应性控制方法,使用马车极平衡模型加以证明。