In this paper, three computationally proficient model predictive control (MPC) algorithms for least square support vector machine (LSSVM)-based Wiener model are described. A Wiener model with Laguerre filter as dynamic linear part and LSSVM approximator as nonlinear static part is considered. Even though having excellent approximation abilities, LSSVM suffers from lack of sparseness. A pruning algorithm for LSSVM model is proposed and its comparison is made with classical pruning algorithm. The proposed pruning algorithm is able to remove 99% of support vectors with no remarkable drop in modelling accuracy. Using pruned Wiener model, three computationally efficient MPC algorithms are described. In the first algorithm, linearization of Wiener model is performed at every sampling interval and therefore control vector is determined by carrying out a quadratic optimization task. In the second algorithm, control signal is determined by an explicit control law and parameters of this control law are computed by performing lower-upper (LU) factorization of a matrix and solving linear equations without any online optimization. In the third algorithm, the parameters of explicit control law are calculated directly by another LSSVM approximator, which is trained offline. The advantages and effectiveness of proposed methods are demonstrated on the benchmark pH neutralization reactor. The control performance and computational efficiency of proposed algorithms are compared with computationally complex nonlinear MPC, which repeats a nonlinear optimization task at every sampling interval. The impact of pruning on model accuracy, computational efficiency and control accuracy is also discussed.

本文介绍了基于最小二乘支持向量机（LSSVM）的Wiener模型的三种计算熟练的模型预测控制（MPC）算法。考虑了以拉盖尔滤波器为动态线性部分，以LSSVM近似器为非线性静态部分的Wiener模型。即使具有出色的逼近能力，LSSVM也缺乏稀疏性。提出了一种针对LSSVM模型的修剪算法，并将其与经典修剪算法进行了比较。提出的修剪算法能够删除99％的支持向量，而建模精度没有明显下降。使用修剪的维纳模型，描述了三种计算有效的MPC算法。在第一种算法中 在每个采样间隔执行Wiener模型的线性化，因此通过执行二次优化任务来确定控制向量。在第二种算法中，控制信号由明确的控制定律确定，并且该控制定律的参数是通过对矩阵执行上下限（LU）分解并求解线性方程式而无需任何在线优化来计算的。在第三种算法中，显式控制律的参数直接由另一个经过离线训练的LSSVM逼近器直接计算。在基准pH中和反应器上证明了所提出方法的优点和有效性。将所提算法的控制性能和计算效率与计算复杂的非线性MPC进行比较，在每个采样间隔重复一次非线性优化任务。还讨论了修剪对模型精度，计算效率和控制精度的影响。