一种基于质点动力学原理的快速自适应建模算法

Novel Fast Adaptive Modeling Algorithm Based on Particle Dynamics

针对自适应逆控制技术中最小均方(LMS)算法建模速度慢的缺点,基于重力场中超曲面上质点的动力学原理,提出了一种快速自适应建模算法.该算法的特点是将滤波器权系数的迭代求解过程类比为重力场中超曲面上质点的运动,在质点的自由运动微分方程中加入比例阻尼项,使各模态的阻尼系数均接近于临界阻尼,从而使权系数以较快速度收敛,并利用质点微分方程中的非线性项实现变步长迭代,明显提高了自适应维纳滤波器的权系数收敛速度.仿真试验结果证明该算法优于LMS算法.该算法运算代价小,收敛速度快,可替代LMS算法用作自适应逆控制的建模工具.

A new adaptive modeling algorithm, PDMDF (proportionally damped multidegree of freedom system), is proposed to build the model of a plant. It is derived by assimilating the process of iteration for the optimal weight coefficients to a particle movement on the hypersurface, the mean square error surface geometry in the space of filter parameters located in the gravitational field. The PDMDF algorithm is developed from the partial differential equation by introducing a proportional damping force and making all damping factors approach the critical damping. The nonlinear term in the partial differential equation is considered as a variable step size in the PDMDF algorithm. The simulation results show a faster convergence rate of the algorithm than that of least mean square algorithm at the same level of misadjustment. This new algorithm could be expected to apply to adaptive inverse control.