Switching Control of Nonlinear Systems Based on the Quasi-ARX Model and the SVR Algorithm
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摘要:
该文基于改进的含有外部输入项的准线性自回归(准ARX)径向基函数(RBF)网络模型和支持向量回归(SVR)算法，提出了一种非线性切换控制方法。 改进的准ARX模型非线性部分采用RBF网络。 控制系统设计过程分为三个部分：首先，利用聚类方法确定模型的非线性参数；然后，采用线性SVR算法来解决控制系统的鲁棒性问题；接下来，基于控制误差给出切换判定函数，确定切换律给出控制序列。 最后通过数值仿真验证了该方法的有效性。
Abstract:A nonlinear switching control method was proposed based on an improved quasilinear autoregressive with exogenous inputs (quasi-ARX) radial basis function (RBF) network model and the support vector regression (SVR) algorithm. The RBF network was chosen as the nonlinear part of the improved quasi-ARX prediction model. The proposed controller design method was divided into 3 steps: firstly, the nonlinear parameters of the model were determined with the clustering method; secondly, the linear SVR algorithm was used to solve the robustness problem of the control system; thirdly, the switching criterion function was given based on the control error, and the control sequence were determined according to the switching law. Finally, a numerical example was given to verify the effectiveness of the proposed method.
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Key words:
- quasi-ARX model /
- stability /
- support vector regression /
- nonlinear switching control
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图 1 仿真例子的控制结果图：(a) 控制输出
$ y(t) $ ，期望输出$ y^*(t) $ ；(b) 输入序列$ u(t) $ ；(c)切换序列$ \chi(t) $ Figure 1. Control results of the example: (a) control output
$ y(t) $ and desired output$ y^*(t) $ ; (b) control input$ u(t) $ ; (c) switching sequence$ \chi(t) $ 表 1 基于噪声
$ v(t) $ 情况下控制误差对比表$ v(t) $ Table 1. Comparison of errors with the noise
mean of errors variance of errors linear control $-0.115 \;0$ $0.095\;3$ NN control $-0.010\;3$ $0.008\;0$ third control $-0.016\;3$ $0.007\;5$ proposed control $-0.004\;3$ $0.005\;3$ 
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