论文标题
神经系统水平综合：对非线性系统的所有稳定政策的学习
Neural System Level Synthesis: Learning over All Stabilizing Policies for Nonlinear Systems
论文作者
论文摘要
我们解决了在离散时间设计稳定控制策略的问题，同时最大程度地减少了任意成本函数。当系统是线性的并且成本为凸面时，系统级别合成（SLS）方法提供了基于凸编程的有效解决方案。除这种情况外，总体上无法以易于处理的方式找到全球最佳解决方案。在本文中，我们根据1）稳定稳定的基础控制器的组合效应以及2）自由设计的稳定的SLS操作员的组合效应来开发所有和仅控制稳定给定时间变化的非线性系统的参数化。基于此结果，我们提出了一种神经SLS（Neur-SLS）方法，以确保参数优化期间和之后的闭环稳定性，而无需满足任何约束。我们利用基于复发均衡网络（RENS）的最新深神经网络（DNN）模型来学习一类丰富的非线性稳定操作员，并在数值示例中证明了拟议方法的有效性。
We address the problem of designing stabilizing control policies for nonlinear systems in discrete-time, while minimizing an arbitrary cost function. When the system is linear and the cost is convex, the System Level Synthesis (SLS) approach offers an effective solution based on convex programming. Beyond this case, a globally optimal solution cannot be found in a tractable way, in general. In this paper, we develop a parametrization of all and only the control policies stabilizing a given time-varying nonlinear system in terms of the combined effect of 1) a strongly stabilizing base controller and 2) a stable SLS operator to be freely designed. Based on this result, we propose a Neural SLS (Neur-SLS) approach guaranteeing closed-loop stability during and after parameter optimization, without requiring any constraints to be satisfied. We exploit recent Deep Neural Network (DNN) models based on Recurrent Equilibrium Networks (RENs) to learn over a rich class of nonlinear stable operators, and demonstrate the effectiveness of the proposed approach in numerical examples.
