中文摘要：

为提高广义预测控制系统的实时性，基于Toeplitz变换提出了广义预测控制（GPC）逆矩阵的快速算法。在预测时域N和控制时域M相等与不相等两种情况下，将控制律求逆部分变换成Toeplitz形式，采用Trench—Zohar求逆算法和下三角矩阵求逆算法快速求取变换后的逆矩阵。分析表明，该算法计算量比常规求逆计算低一阶，并且步骤简便，容易编程实现。实验研究验证了该算法的有效性。

英文摘要：

Based on Toeplitz transformation, a fast algorithm for inverse matrix in generalized predictive control （GPC） is presented in order to improve the real-time ability of the system. Under two conditions that prediction horizon N is equal and not equal to control horizon M, inverse matrix in the control law is transformed into Toeplitz matrix form; then the Trench-Zohar algorithm and the inversion algorithm of lower triangular matrix are applied to calculate the transformed inverse matrix quickly. Algorithm analysis indicates that the computational load of the above algorithm is one order less than that of conventional algorithm. Moreover, the method is not only simple, but also easy to be programmed. The validity of this algorithm is verified by experiment research.