AI 中文总结
研究一阶线性双曲型平衡律在一般驱动下的指数镇定，提出统一方法，整合多种欠驱动配置，应用于含环网络，基于反步变换和积分差分方程设计控制律，增益由降秩程序和插值方程解构建，通过数值模拟验证对特定循环网络的有效性。
AI 中文摘要
本文针对一般驱动情况下的一阶线性双曲型平衡律的指数镇定开发了一种统一方法，包括欠驱动边界控制和域内控制。所提出的框架将多种欠驱动配置整合在一个公式中，极大地扩展了现有局限于特定驱动设置的结果。利用切割和折叠变换，该方法进一步应用于双曲型平衡律网络，包括有环的配置。控制设计在可镇定性条件和鲁棒性假设下进行，基于可逆反步变换，部分解耦系统，然后在积分差分方程层面重新表述镇定问题。通过结合稳定的降秩程序和来自科罗纳问题的插值方程解来构建动态反馈律的增益。给出了现有文献方法无法处理的相关循环网络的数值模拟。
英文摘要
This paper develops a unified method for the exponential stabilization of first-order linear hyperbolic balance laws under general actuation, including both underactuated boundary and in-domain control. The proposed framework brings together a wide range of underactuated configurations within a single formulation and substantially extends existing results restricted to particular actuation settings. Using cutting and folding transformations, the proposed approach is further applied to networks of hyperbolic balance laws, including configurations with cycles. The control design is developed under a stabilizability condition and a robustness assumption. It is based on an invertible backstepping transformation, which partially decouples the system, followed by a reformulation of the stabilization problem at the level of an Integral Difference Equation (IDE). The gains of the resulting dynamic feedback law are constructed at the IDE level by combining a stable rank-reduction procedure, which reduces the problem to a single-input design, with the solution of an interpolation equation arising from a Corona problem. Numerical simulations are presented for a relevant cycle network that cannot be addressed by existing methods in the literature.
