Robust stability of fuzzy logic control systems
Robust stability of fuzzy logic control systems
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模糊逻辑控制系统的鲁棒稳定性
DOI：
10.1109/acc.1995.531375
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发表时间：
1995
期刊：
影响因子：
--
通讯作者：
George Vachtsevanos
中科院分区：
文献类型：
--
作者：
Farinwata;George Vachtsevanos
提出了一种用模糊逻辑分析一大类线性和非线性系统性能的近似方法。假定有标称装置的近似模型可用。考虑了在存在小的有界参数不确定性和已知来源的外部扰动的情况下的稳定性。该方法基于将性能度量适当地表示为标称对象的类Lyapunov函数。系统相对于感兴趣的参数的误差灵敏度的启发式测量被合并到要最小化的该性能表达式中。应用类Lyapunov稳定性条件，通过观察简单矩阵的正定性条件，分析了系统的鲁棒性。该理论分两部分展开。首先，假设状态是解耦的，即特定状态中的参数扰动不会对其他状态产生影响。在此基础上，给出了主要的鲁棒稳定性结果。在第二部分中，由于参数的变化，允许状态之间存在某种相互作用。对相互作用的量度的估计是基于稳定性的。然后，给出了一个更一般的鲁棒稳定性结果。稳定收敛点是系统指定的目标点。因此，在存在参数摄动和外部负载的情况下，稳定性收敛到这一点本身就解决了闭环系统的鲁棒稳定性问题。最后用模糊量的形式给出了灵敏度、误差偏差和参数偏差的不等式界。然后使用奇异值来表示稳健性的度量。以汽车发动机怠速模糊控制器为例，说明了该方法的有效性。
An approximate method is formulated for analyzing the performance of a broad class of linear and nonlinear systems controlled using fuzzy logic. It is assumed that an approximate model of the nominal plant is available. Stability in the presence of small, bounded parametric uncertainty and external disturbance of a known origin is considered. The method is based on an appropriate formulation of a performance measure as a Lyapunov-like function of the nominal plant. A heuristic measure of the system's error sensitivity with respect to the parameters of interest is incorporated into this performance expression which is to be minimized. By applying a Lyapunov-like stability condition, the robustness of the system is analyzed by observing a definiteness condition of a simple matrix. The theory is developed in two parts. First, it is assumed that the states are decoupled in the sense that a parameter perturbation in a particular state has no effect on other states. The main robust stability result is developed based on this assumption. In the second part, some interaction is allowed to exist between states as a result of parameter variation. Estimates of the measure of the interactions are derived on stability grounds. A more general result for robust stability is then given. The point of stability convergence is the system's specified target point. Thus, stability convergence to this point, in the presence of parameter perturbations and external load inherently addresses the robust stability of the closed-loop system. Finally, inequality bounds are derived for the sensitivity, error deviation and parameter deviations in terms of fuzzy quantities. A measure for robustness is then formulated using singular values. A fuzzy automotive engine idle speed controller is used to illustrate the methodology.