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Performance assessment of fuzzy logic control systems via stability and robustness measures.

机译：通过稳定性和鲁棒性评估模糊逻辑控制系统的性能。

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A viable control theoretic technique was developed for assessing the performance of fuzzy logic control systems. Stability and robustness were considered as measures of the closed loop system's performance. Essentially, the fuzzy logic controller (FLC) in the closed loop system generated the control inputs necessary to control the process, whose mathematical model was readily available. The stability theories developed were of the input-output type. The fuzzy controller was required to drive the system from all initial conditions in the feasible state space, asymptotically to the origin, which is the unique zero-error point. In the first of the two stability theories developed, input-output mappings were formulated linear and nonlinear processes. Essentially, a Lyapunov-like function was assumed, which measures the energy of the physical process that was being fuzzily controlled. From this, the output variables were identified and included in the time derivative of the Lyapunov-like function. In the case of the linear process, on the other hand, the input-output mapping was readily formed in the standard way, using the system's time invariant matrices, and the same stability condition was imposed on the mapping. Alternatively, the Kalman-Yakubovich (Positive Real) lemma was proposed, when the linear system was open-loop stable. The second stability analysis proposed for the fuzzy controlled systems pertained to process set-point control systems. The growth of nonlinearity away from this set-point vicinity was required to diminish under fuzzy control. A set of controllability conditions of fuzzy control systems was proposed that using strictly, the fuzzy if-then rules and the discrete-time fuzzy dynamical system model. On the robustness side, a performance index was formulated based on the system's implicit states. The time derivative was expressed in terms of fuzzy sensitivity functions of the process variables with respect to the parameter perturbations. The first part of the theory was developed with the assumption that the system was decoupled, in the sense that one the parameter for a particular state could be perturbed with no effects on the other system's states. Finally, a set of robust bounds for the parameter perturbations, interactions, and the individual sensitivities were derived. (Abstract shortened by UMI.)
机译：开发了一种可行的控制理论技术来评估模糊逻辑控制系统的性能。稳定性和鲁棒性被认为是闭环系统性能的度量。本质上，闭环系统中的模糊逻辑控制器（FLC）生成了控制过程所需的控制输入，其数学模型很容易获得。所发展的稳定性理论是投入产出型的。需要模糊控制器来将系统从可行状态空间中的所有初始条件渐近驱动到原点（即唯一的零误差点）。在所开发的两种稳定性理论中的第一种中，输入-输出映射被表述为线性和非线性过程。本质上，假定了一个类似Lyapunov的函数，该函数可测量模糊控制的物理过程的能量。由此确定输出变量，并将其包含在类Lyapunov函数的时间导数中。另一方面，在线性过程的情况下，使用系统的时不变矩阵可以很容易地以标准方式形成输入-输出映射，并且对映射施加相同的稳定性条件。另外，当线性系统是开环稳定的时，提出了Kalman-Yakubovich（正实数）引理。针对模糊控制系统提出的第二种稳定性分析涉及过程设定点控制系统。在模糊控制下，需要减小远离此设定点附近的非线性的增长。提出了一套模糊控制系统的可控制性条件，严格使用了模糊If-then规则和离散时间模糊动力学系统模型。在健壮性方面，基于系统的隐式状态制定了性能指标。时间导数用过程变量相对于参数摄动的模糊灵敏度函数表示。该理论的第一部分是在假设系统已解耦的前提下开发的，从某种意义上说，一个特定状态的参数可能会受到干扰，而不会影响其他系统的状态。最后，得出了一组针对参数摄动，相互作用和个体敏感性的鲁棒边界。 （摘要由UMI缩短。）

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