A multi-objective linear-programming-based four-judgment modeling algorithm is proposed for an unknown but bounded noise system. Because there is no prior knowledge about the bounded noise term, during each recursive step, the noise signal is warped in a strip and the hyperplanes can be obtained by samples of input and output signals. The feasible parameter set of a linear discrete-time system with bounded noise, viewed as a convex polytope, is transformed into a polyhedral cone with increasing parameter dimension. One of the vertices of the polyhedral cone is the origin, and the polyhedral vertices can be calculated when the polyhedral cone edge vectors are determined. Moreover, by adopting the multi-objective linear programming idea, a four-judgment modeling algorithm is proposed for linear discrete-time systems. The given simulations illustrate the feasibility and effectiveness of the given algorithm.

针对未知但有界的噪声系统，提出了一种基于多目标线性规划的四判断建模算法。由于没有关于有界噪声项的先验知识，因此在每个递归步骤中，噪声信号会在一条带中弯曲，并且超平面可以通过输入和输出信号的采样获得。将具有离散噪声的线性离散时间系统的可行参数集（视为凸多面体）转换为参数尺寸增大的多面圆锥体。多面圆锥体的顶点之一是原点，并且当确定多面体圆锥体边缘矢量时，可以计算多面体顶点。此外，通过采用多目标线性规划思想，提出了一种针对线性离散时间系统的四判断建模算法。