In this paper,we give the explicit expressions of level k (r 1,r 2,…,r k) circulant matrices of order n 1n 2…n k,and the explicit expressions for the eigenvalues,the determinants and the inverse matrices of the kind...In this paper,we give the explicit expressions of level k (r 1,r 2,…,r k) circulant matrices of order n 1n 2…n k,and the explicit expressions for the eigenvalues,the determinants and the inverse matrices of the kind level k (r 1,r 2,…,r k) circulant matrices are derived,and it is also proved that the sort of matrices are diagonalizable.展开更多
针对车辆主动悬架系统的线性二次型调节器(linear quadratic regulator,LQR)在设定权重系数矩阵Q和R时具有主观性、效率低的缺点,提出一种基于蛇算法(snake optimizer,SO)优化LQR控制器权重系数矩阵的策略。通过对1/4车辆主动悬架系统...针对车辆主动悬架系统的线性二次型调节器(linear quadratic regulator,LQR)在设定权重系数矩阵Q和R时具有主观性、效率低的缺点,提出一种基于蛇算法(snake optimizer,SO)优化LQR控制器权重系数矩阵的策略。通过对1/4车辆主动悬架系统的动力学分析,设计了LQR控制器;将主动悬架与被动悬架各性能指标的积分比值进行加权求和构建了目标函数L;模仿蛇群生活习性的SO算法在搜索空间中求解出了函数L的最小值和LQR控制器的最优权重系数矩阵。为验证该策略的有效性,分别以C级路面、正弦冲击路面为激励,对车身加速度(sprung mass acceleration,SMA)、轮胎动载荷(dynamic tyre load,DTL)、悬架动行程(suspension working space,SWS)3个方面将SO优化LQR控制的主动悬架与被动悬架、传统LQR控制的主动悬架、遗传算法优化LQR控制的主动悬架、粒子群算法优化LQR控制的主动悬架进行了仿真对比。结果表明:SO优化LQR控制的主动悬架可在C级路面上分别对SMA、DTL、SWS的均方根优化达59.47%、37.89%、42.12%;在正弦冲击路面上稳定时间为1.4 s,分别对SMA、DTL、SWS的超调优化达79.21%、59.22%、16.33%,提升了车辆的行驶平顺性、路面附着性和操作安全性。展开更多
In this paper,we describe multiplicative derivations on the set of all rank-s matrices of Mn(K)over a field K with a relatively small integer s.Concretely,for fixed integers n,s satisfying 1≤s≤n/2 and n≥2,we prove ...In this paper,we describe multiplicative derivations on the set of all rank-s matrices of Mn(K)over a field K with a relatively small integer s.Concretely,for fixed integers n,s satisfying 1≤s≤n/2 and n≥2,we prove that if a map d:Mn(K)→Mn(K)satisfiesδ(xy)=δ(x)y+xδ(y)for any two rank-s matrices,y∈Mn(K),then there exists a derivation D of Mn(K)such thatδ(x)=D(x)for each rank-k matrix a E Mn(K)with 0≤k≤s.As an application,we prove that a multiplicative derivation on a special subset of Mn(K)must be a derivation.展开更多
文摘In this paper,we give the explicit expressions of level k (r 1,r 2,…,r k) circulant matrices of order n 1n 2…n k,and the explicit expressions for the eigenvalues,the determinants and the inverse matrices of the kind level k (r 1,r 2,…,r k) circulant matrices are derived,and it is also proved that the sort of matrices are diagonalizable.
文摘针对车辆主动悬架系统的线性二次型调节器(linear quadratic regulator,LQR)在设定权重系数矩阵Q和R时具有主观性、效率低的缺点,提出一种基于蛇算法(snake optimizer,SO)优化LQR控制器权重系数矩阵的策略。通过对1/4车辆主动悬架系统的动力学分析,设计了LQR控制器;将主动悬架与被动悬架各性能指标的积分比值进行加权求和构建了目标函数L;模仿蛇群生活习性的SO算法在搜索空间中求解出了函数L的最小值和LQR控制器的最优权重系数矩阵。为验证该策略的有效性,分别以C级路面、正弦冲击路面为激励,对车身加速度(sprung mass acceleration,SMA)、轮胎动载荷(dynamic tyre load,DTL)、悬架动行程(suspension working space,SWS)3个方面将SO优化LQR控制的主动悬架与被动悬架、传统LQR控制的主动悬架、遗传算法优化LQR控制的主动悬架、粒子群算法优化LQR控制的主动悬架进行了仿真对比。结果表明:SO优化LQR控制的主动悬架可在C级路面上分别对SMA、DTL、SWS的均方根优化达59.47%、37.89%、42.12%;在正弦冲击路面上稳定时间为1.4 s,分别对SMA、DTL、SWS的超调优化达79.21%、59.22%、16.33%,提升了车辆的行驶平顺性、路面附着性和操作安全性。
基金supported by the NSF of China(grants No.11971289,No.11771176)Wang Yanhua was supported by the NSF of China(grant No.11971289)+1 种基金Zhao Zhibing was supported by the NSF of China(grant No.11571329)the Project of University Natural Science Research of Anhui Province(grant No.KJ2019A0007).
文摘In this paper,we describe multiplicative derivations on the set of all rank-s matrices of Mn(K)over a field K with a relatively small integer s.Concretely,for fixed integers n,s satisfying 1≤s≤n/2 and n≥2,we prove that if a map d:Mn(K)→Mn(K)satisfiesδ(xy)=δ(x)y+xδ(y)for any two rank-s matrices,y∈Mn(K),then there exists a derivation D of Mn(K)such thatδ(x)=D(x)for each rank-k matrix a E Mn(K)with 0≤k≤s.As an application,we prove that a multiplicative derivation on a special subset of Mn(K)must be a derivation.
