Robust global stabilization of linear systems with input saturation via gain scheduling
Robust global stabilization of linear systems with input saturation via gain scheduling
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DOI：
10.1002/rnc.1436
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发表时间：
2010-03
影响因子：
3.9
通讯作者：
Bin Zhou;Zongli Lin;G. Duan
中科院分区：
文献类型：
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作者：
Bin Zhou;Zongli Lin;G. Duan
本文重新讨论了受输入饱和和输入加性不确定性影响的线性系统的鲁棒全局稳定性问题。利用最近开发的基于参数Lyapunov方程的低增益反馈设计方法和现有的动态增益调度技术，提出了一种新的增益调度控制器来解决该问题。与现有的ℋ2型增益调度控制器相比，该控制器需要在线求解状态相关的非线性优化问题和状态相关的ℋ2代数Riccati方程（ARE），所提出的控制器中的所有参数都是先验确定的。在不存在输入加性不确定性的情况下，所提出的控制器还通过解决具有执行器饱和的线性系统的全局稳定性问题来部分恢复Teel的ℋ∞型调度方法。 ℋ∞型调度方法不仅在非输入可加不确定性下实现了鲁棒性，而且还需要ℋ∞ ARE的封闭式解。因此，所提出的调度方法还解决了在不存在非输入可加不确定性的情况下ℋ∞型调度方法的实现问题。版权所有 © 2009 约翰·威利父子有限公司
The problem of robust global stabilization of linear systems subject to input saturation and input‐additive uncertainties is revisited in this paper. By taking advantages of the recently developed parametric Lyapunov equation‐based low gain feedback design method and an existing dynamic gain scheduling technique, a new gain scheduling controller is proposed to solve the problem. In comparison with the existing ℋ2‐type gain scheduling controller, which requires the online solution of a state‐dependent nonlinear optimization problem and a state‐dependent ℋ2 algebraic Riccati equation (ARE), all the parameters in the proposed controller are determined a priori. In the absence of the input‐additive uncertainties, the proposed controller also partially recovers Teel's ℋ∞‐type scheduling approach by solving the problem of global stabilization of linear systems with actuator saturation. The ℋ∞‐type scheduling approach achieves robustness not only with non‐input‐additive uncertainties but also requires the closed‐form solution to an ℋ∞ ARE. Thus, the proposed scheduling method also addresses the implementation issues of the ℋ∞‐type scheduling approach in the absence of non‐input‐additive uncertainties. Copyright © 2009 John Wiley & Sons, Ltd.