Two modified fast algorithms of generalized predictive control (GPC) based on Toeplitz transformation are proposed. Firstly, the complex computation of matrix inversion is avoided by introducing a kind of softing coefficient matrix into the existing GPC algorithm based on Toeplitz transformation and without solving Diophantine Equation, which further improves the operation efficiency of algorithm. Secondly, the existing GPC algorithm based on Toeplitz transformation and with solving Diophantine Equation is extended to the case that prediction horizon is not equal to control horizon for matrix transformation, which expands the applied scope of algorithm. The simulated results show the effectiveness of the above algorithms.%提出两种改进的Toeplitz变换广义预测控制快速算法.其一,在已有无需Diophantine方程求解的Toeplitz变换广义预测控制算法中引入一种柔化矩阵,避免了复杂的矩阵求逆计算,进一步提高了算法的快速性；其二,通过矩阵变换,将现有基于Diophantine方程求解的Toeplitz变换广义预测控制算法推广到预测时域和控制时域不相等情况,扩展了算法的适用范围.仿真结果验证了上述算法的有效性.
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