Almost restoring problem of deterministic asymptotic stability against additive noises
Almost restoring problem of deterministic asymptotic stability against additive noises
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DOI：
10.1109/cca.2014.6981469
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发表时间：
2014-12
期刊：
影响因子：
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通讯作者：
Y. Nishimura
中科院分区：
文献类型：
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作者：
Y. Nishimura
本文提出了一种针对加性高斯白噪声的非线性受控系统的干扰抑制策略。为了达到这一目的，我们首先回顾了随机系统的下列随机稳定性概念：一致几乎处处渐近稳定(UASAS)、指数p-稳定性和有限时间概率稳定性。结合前面的概念，我们提出了新的渐近稳定性性质和新的随机Lyapunov函数，p-稳定性关于(W.r.t.)EV和拟几乎李雅普诺夫函数(拟ALF)，得到了在原点具有非零值的随机扰动项的非线性系统的拟ALF。随后，我们提出了一种噪声表面控制策略，以获得使随机系统几乎恢复其不受加性噪声振动时的光滑轨迹的充分条件。通过对具有线性二次型(LQ)控制的随机线性系统的扰动抑制问题的研究，验证了该控制策略的有效性。
This paper proposes a disturbance attenuation strategy for nonlinear controlled systems against the addition of additive Gaussian white noises. To achieve the purpose, we firstly revisit the following stochastic stability notions for stochastic systems: uniform almost sure asymptotic stability (UASAS), exponential p-stability, and finite-time stability in probability. Combining the previous notions, we propose new asymptotic stability properties and new stochastic Lyapunov functions, p-stability with respect to (w.r.t.) EV, and quasi almost Lyapunov functions (quasi-ALFs) for nonlinear systems with stochastic disturbance terms, the values of which are nonzero at the origins. Subsequently, we propose a strategy of noisy surface control to obtain sufficient conditions so that stochastic systems almost restore their smooth trajectories of the time when they were not vibrated by additive noises. The effectiveness of the control strategy is confirmed by the consideration of disturbance attenuation problems for stochastic linear systems with linear quadratic (LQ) controls.