椭球状态定界的鲁棒算法

Robust ellipsoidal state bounding algorithm

提出了一种计算鲁棒的线性离散时间系统的椭球状态定界算法.算法假设系统的过程和量测噪声以及初始状态由已知椭球来定界,然后利用椭球集合来描述系统真实状态的可行集.算法的时间更新和量测更新过程分别产生两个椭球的向量和与交.算法对椭球形状矩阵进行Cholesky分解,使得当存在舍入误差时椭球形状矩阵保持正定.为了不受病态矩阵求逆的影响,算法的量测更新过程采用了求次最小容积椭球的方法.采用在数字计算机上进行蒙特卡洛仿真来检验算法的性能.结果表明算法的精度与最优算法十分接近,并且具有很好的计算鲁棒性.算法同时具有易于在并行计算机上运行的优点.

A numerically robust algorithm for computing ellipsoidal bounds on the state of a linear, discrete - time dynamic system was proposed. The algorithm employed ellipsoidal outer approximation of the feasible set assuming instantaneous process and observation noise vectors and the initial state to be bounded by known ellipsoids. The time and observation updates produced, respectively, the vector sum and intersection of two ellipsoids. Cholesky decomposition was used in the propagation of the shape - defining matrix of the ellipsoid to keep it positive definite in the presence of roundoff errors. Besides, a subminimal - volume ellipsoid was selected from a family of ellipsoids as the observation - updated ellipsoid to circumvent the complex optimization affected by ill -conditioned matrix inverse. Monte Carlo simulations on a digital computer were performed to compare the performance of the proposed algorithm with that of the optimal algorithm. Simulation resuits show that the proposed algorithm not only matches the performance of the optimal algorithm closely in terms of ellipsoid volumes and mean-square errors, but also is less vulnerable to roundoff errors. The proposed algorithm also features the capability to be realized on a parallel computer.