The finite‐time stabilization and H_∞ control of stochastic nonlinear systems was investigated in this article. First, we discussed the relationship between the finite‐time stability and the dissipation property by transforming the stochastic nonlinear system to its equivalent Hamiltonian formulation. It was showed that the stochastic dissipative Hamiltonian system is finite‐time stable in probability if the system is strictly dissipative and the Hamiltonian function possessed some special forms. Then, by the energy shaping and damping injection technique, we reformulate the internal structure matrix and the Hamiltonian function to construct a finite‐time stabilization controller for stochastic nonlinear systems. Moreover, for uncertain stochastic nonlinear systems, an H_∞ finite‐time robust controller was put forward by utilizing the Hamiltonian function to construct a solution for the Hamiltonian‐Jacobi Inequality. Finally, we proposed a finite‐time stabilization and a finite‐time H_∞ controller for the inverted cart‐pendulum system to verify the effectiveness of the proposed method.

中文翻译：

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随机非线性系统基于能量的有限时间稳定和H∞控制

的有限时间稳定和ħ _∞随机非线性系统的控制在本文中进行了研究。首先，我们通过将随机非线性系统转换为其等效的哈密顿量公式，讨论了有限时间稳定性与耗散特性之间的关系。结果表明，随机耗散哈密顿系统在严格耗散且哈密顿函数具有某些特殊形式的情况下，具有一定的时间稳定性。然后，通过能量整形和阻尼注入技术，我们重新构造了内部结构矩阵和哈密顿函数，以构造用于随机非线性系统的有限时间稳定控制器。此外，不确定随机非线性的系统中，ħ _∞提出了利用哈密顿函数构造哈密顿雅可比不等式的有限时鲁棒控制器。最后，我们提出了一个有限时间稳定和一个有限时间ħ _∞控制器，用于倒车摆系统，以验证所提出的方法的有效性。