Title: Boosting the transient performance of reference tracking controllers with neural networks Show Chinese title

Title: 利用神经网络提升参考跟踪控制器的瞬态性能

Abstract: Reference tracking is a key objective in many control systems, including those characterized by complex nonlinear dynamics. In these settings, traditional control approaches can effectively ensure steady-state accuracy but often struggle to explicitly optimize transient performance. Neural network controllers have gained popularity due to their adaptability to nonlinearities and disturbances; however, they often lack formal closed-loop stability and performance guarantees. To address these challenges, a recently proposed neural-network control framework known as Performance Boosting (PB) has demonstrated the ability to maintain $\mathcal{L}_p$ stability properties of nonlinear systems while optimizing generic transient costs. This paper extends the PB approach to reference tracking problems. First, we characterize the complete set of nonlinear controllers that preserve desired tracking properties for nonlinear systems equipped with base reference-tracking controllers. Then, we show how to optimize transient costs while searching within subsets of tracking controllers that incorporate expressive neural network models. Furthermore, we analyze the robustness of our method to uncertainties in the underlying system dynamics. Numerical simulations on a robotic system demonstrate the advantages of our approach over the standard PB framework. Show Chinese abstract

Abstract: 参考跟踪是许多控制系统的一个关键目标，包括那些具有复杂非线性动态特性的系统。在这些场景中，传统的控制方法能够有效地确保稳态精度，但往往难以明确优化瞬态性能。由于神经网络控制器能够适应非线性和干扰，因此广受欢迎；然而，它们通常缺乏形式化的闭环稳定性和性能保证。为了解决这些挑战，最近提出的一种名为性能提升（PB）的神经网络控制框架展示了在保持非线性系统的$\mathcal{L}_p$稳定特性的同时优化通用瞬态成本的能力。本文将 PB 方法扩展到参考跟踪问题上。首先，我们描述了完整的一组非线性控制器，这些控制器能够保持带有基础参考跟踪控制器的非线性系统的期望跟踪属性。然后，我们展示了如何在包含表达性强的神经网络模型的跟踪控制器子集内搜索时优化瞬态成本。此外，我们分析了我们的方法对底层系统动力学不确定性的影响。机器人系统的数值模拟表明，与标准 PB 框架相比，我们的方法具有优势。