AI 中文总结
研究通过最优控制实现线性系统有限时间稳定的问题，核心方法是引入积分成本函数推导新非线性控制器，主要贡献为得到最优控制律与值函数关系、导出HJB方程，数值模拟验证方法有效性并讨论收敛时间估计。
AI 中文摘要
本文提出了一个用于实现线性系统有限时间稳定的最优控制框架。通过引入适当构造的积分成本函数，我们推导出一类新的非线性控制器，通过应用最优性原理保证有限时间稳定性。分析了所得最优控制律与相关值函数之间的关系，导出了汉密尔顿-雅可比-贝尔曼（HJB）方程并研究其正则性。数值模拟验证了理论结果并说明了该方法的有效性。此外，还提供了关于收敛时间估计的讨论。
英文摘要
This paper presents an optimal control framework for achieving finite-time stabilization of linear systems. By introducing a suitably constructed integral cost function, we derive a new class of nonlinear controllers that guarantee finite-time stability through the application of the optimality principle. The relationship between the resulting optimal control law and the associated value function is analyzed, leading to the derivation of a Hamilton-Jacobi-Bellman (HJB) equation and the study of its regularity properties. Numerical simulations validate the theoretical findings and illustrate the effectiveness of the proposed method. Furthermore, a discussion on estimating the convergence time is provided.
