标题： 应对意外情况：稳定设计的神经反馈控制与Youla-REN 显示英文标题

标题： React to Surprises: Stable-by-Design Neural Feedback Control and the Youla-REN

摘要： 我们研究了基于学习的控制中稳定非线性策略的参数化方法。 我们提出了一种基于非线性Youla-Kucera参数化结构，并结合了诸如递归平衡网络（REN）之类的鲁棒神经网络。 由此产生的参数化是无约束的，因此可以通过一阶优化方法进行搜索，同时通过构造始终确保闭环稳定性。 我们研究了以下三者的组合：(a) 非线性动力学，(b) 部分观测，以及(c) 增量闭环稳定性要求（收缩性和Lipschitz性质）。 我们发现，只要有其中的两个困难存在，收缩型和Lipschitz型Youla参数总是会导致收缩型和Lipschitz型闭环。然而，如果三个条件都成立，则会因外部干扰而失去增量稳定性。 相反，我们维持了一个较弱的条件，我们称之为d-tube收缩性和Lipschitz性质。 我们进一步得到了逆向结果，表明所提出的参数化涵盖了某些非线性系统类别的所有收缩型和Lipschitz型闭环。 数值实验表明了我们参数化的实用性，特别是在以下情况下：(i) "经济"奖励但没有稳定效果；(ii) 短训练周期；以及(iii) 不确定系统。 显示英文摘要

摘要： We study parameterizations of stabilizing nonlinear policies for learning-based control. We propose a structure based on a nonlinear version of the Youla-Kucera parameterization combined with robust neural networks such as the recurrent equilibrium network (REN). The resulting parameterizations are unconstrained, and hence can be searched over with first-order optimization methods, while always ensuring closed-loop stability by construction. We study the combination of (a) nonlinear dynamics, (b) partial observation, and (c) incremental closed-loop stability requirements (contraction and Lipschitzness). We find that with any two of these three difficulties, a contracting and Lipschitz Youla parameter always leads to contracting and Lipschitz closed loops. However, if all three hold, then incremental stability can be lost with exogenous disturbances. Instead, a weaker condition is maintained, which we call d-tube contraction and Lipschitzness. We further obtain converse results showing that the proposed parameterization covers all contracting and Lipschitz closed loops for certain classes of nonlinear systems. Numerical experiments illustrate the utility of our parameterization when learning controllers with built-in stability certificates for: (i) "economic" rewards without stabilizing effects; (ii) short training horizons; and (iii) uncertain systems.