Abstract When piecewise affine (PWA) model-based control methods are applied to nonlinear systems, the first question is how to get sub-models and corresponding operating regions. Motivated by the fact that the operating region of each sub-model is an important component of a PWA model and the parameters of a sub-model are strongly coupled with the operating region, a new PWA model identification method based on optimal operating region partition with the output-error minimization for nonlinear systems is initiated. Firstly, construct local data sets from input-output data and get local models by using the least square (LS) method. Secondly, cluster local models according to the feature vectors and identify the parameter vectors of sub-models by weighted least squares (WLS) method. Thirdly, get the initial operating region partition by using a normalized exponential function, which is to partition the operating space completely. Finally, simultaneously determine the optimal parameter vectors of sub-models and the optimal operating region partition underlying the output-error minimization, which is executed by particle swarm optimization (PSO) algorithm. Simulation results demonstrate that the proposed method can improve model accuracy compared with two existing methods.

中文翻译：

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一种基于输出误差最小化的非线性系统最优操作区域划​​分的PWA模型辨识方法

摘要 当基于分段仿射（PWA）模型的控制方法应用于非线性系统时，第一个问题是如何获得子模型和相应的工作域。考虑到每个子模型的运行区域是 PWA 模型的重要组成部分，并且子模型的参数与运行区域强耦合，一种新的基于最优运行区域划分的 PWA 模型识别方法启动非线性系统的输出误差最小化。首先，从输入输出数据构建局部数据集，并使用最小二乘法（LS）得到局部模型。其次，根据特征向量对局部模型进行聚类，并通过加权最小二乘法（WLS）方法识别子模型的参数向量。第三，使用归一化指数函数得到初始操作区域划​​分，即对操作空间进行完整划分。最后，同时确定子模型的最优参数向量和输出误差最小化的最优操作区域划​​分，由粒子群优化（PSO）算法执行。仿真结果表明，与现有的两种方法相比，所提出的方法可以提高模型精度。