线控转向系统线性自抗扰控制器的群智能优化

魏萱,黄鹤,杨澜,王会峰,高涛

Swarm intelligence optimization of linear active disturbance rejection controller for steer-by-wire system

Xuan WEI,He HUANG,Lan YANG,Huifeng WANG,Tao GAO

表 1 算法性能测试的基准函数

Tab.1 Benchmark function for algorithm performance test

函数 表达式 取值范围 Sphere $f({\boldsymbol{x}}) = \displaystyle \sum\nolimits_{i = 1}^n {x_i^2} $ [−100,100]n Schwefel 2.22 $f({\boldsymbol{x}}) = \displaystyle \sum\nolimits_{i = 1}^n {\left| {{x_i}} \right|} + \displaystyle \prod\nolimits_{i = 1}^n {\left| {{x_i}} \right|} $ [−10,10]n Schwefel 1.2 $f({\boldsymbol{x}}) = {\displaystyle \sum\nolimits_{i = 1}^n {\left( {\displaystyle \sum\nolimits_{j = 1}^i {{x_j}} } \right)} ^2}$ [−100,100]n Schwefel 2.21 $f({\boldsymbol{x}}) = {\max _i}\left\{ {\left| {{x_i}} \right|,1 \leqslant i \leqslant n} \right\}$ [−100,100]n Schwefel $f({\boldsymbol{x}}) = - \displaystyle \sum\nolimits_{i = 1}^n {\left( {{x_i}\sin {\sqrt {\left| {{x_i}} \right|} } } \right)} $ [−500,500]n Ackley $\begin{gathered} f({\boldsymbol{x}}) = - 20\exp \left( { - 0.2\sqrt {{n}^{-1}\sum\nolimits_{i = 1}^n {x_i^2} } } \right) - \exp \left( {{n}^{-1}\sum\nolimits_{i = 1}^n {\cos\; (2{\text{π}}{x_i}}) } \right)+20+{\text{e}} \\ \end{gathered} $ [−32,32]n