Sliding Mode Control in Stochastic Continuos-Time Systems: $\boldsymbol{\mu}$-zone $\boldsymbol{MS}$-Convergence
Sliding Mode Control in Stochastic Continuos-Time Systems: $\boldsymbol{\mu}$-zone $\boldsymbol{MS}$-Convergence
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DOI：
10.1109/tac.2016.2557759
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发表时间：
2017-02
影响因子：
6.8
通讯作者：
A. Poznyak
中科院分区：
文献类型：
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作者：
A. Poznyak
结果表明，滑模控制技术可以成功地应用于由伊藤型随机微分方程所控制的含有加性随机无界白色噪声扰动的随机系统.讨论了相应的随机微分包含强解的存在性。为了使这种方法可行，建议增益控制参数与系统状态的范数相关。结果表明，在这种改进下，我们可以保证滑动变量的平均平方范数指数收敛到与模型描述中的扩散参数$\sigma$成正比、与增益参数$k_{0}$成反比的$\mu$-zone（滑动面周围）.
It is shown that the Sliding Mode Control (SMC) technique can be successfully applied to stochastic systems governed by the stochastic differential equations of the Itô type which contain additive stochastic unbounded white noise perturbations. The existence of a strong solution to the corresponding stochastic differential inclusion is discussed. To do this approach workable the gain control parameter is suggested to be done state-dependent on norms of system states. It is demonstrated that under such modification of the conventional SMC we can guarantee the exponential convergence of the averaged squared norm of the sliding variable to $\mu$-zone (around the sliding surface) which is proportional to the diffusion parameter $\sigma$ in the model description and inversely depending on the gain parameter $k_{0}$.