发表机构
Center for Control Theory and Guidance Technology, Harbin Institute of Technology（控制理论与制导技术研究中心，哈尔滨工业大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出一种嵌套参数李雅普诺夫方程方法，通过构造参数化二次控制李雅普诺夫函数，在仅需求解两个线性矩阵方程且无需实时状态信息的条件下，实现了线性系统在受限控制下的半全局精确预设时间镇定。
AI 中文摘要
本文研究了线性系统在受限控制下的半全局精确预设时间镇定问题。为解决该问题，需要构造一个参数化的二次控制李雅普诺夫函数，其对应的水平集可以任意大（以实现半全局镇定），并且闭环系统极点的实部随着参数趋于无穷而趋于负无穷（以实现预设时间镇定）。通过提出一种基于嵌套参数李雅普诺夫方程（PLE）的方法实现了这一目标，该方法在控制器设计阶段仅需求解两个线性矩阵方程，且无需使用实时状态信息。在所提出的结构条件下，基于嵌套PLE的方法能够保证对于任何给定的有界初始条件集合实现半全局精确预设时间镇定，前提是预设的镇定时间足够大。文中提供了一个数值示例来验证所设计控制器的有效性。
英文摘要
This paper addresses the problem of semi-global exact prescribed-time stabilization of linear systems by bounded controls. To solve such a problem, one needs to construct a parameterized quadratic control Lyapunov function whose corresponding level set can be made arbitrarily large (for achieving semi-global stabilization) and such that the real parts of the poles of the closed-loop system approach minus infinity as the parameter approaches infinity (for achieving prescribed-time stabilization). This objective is achieved by proposing a nested parametric Lyapunov equation (PLE)-based approach, through which only two linear matrix equations need to be solved in the controller design stage without using real-time state information. Under the proposed structural condition, the nested PLE-based approach guarantees semi-global exact prescribed-time stabilization for any prescribed bounded set of initial conditions, provided that the prescribed settling time is sufficiently large. A numerical example is provided to demonstrate the effectiveness of the designed controller.
