This note extends a recently proposed algorithm for model identification and robust model predictive control (MPC) of asymptotically stable, linear time-invariant systems subject to process and measurement disturbances. Independent output predictors for different horizon values are estimated with Set Membership methods. It is shown that the corresponding prediction error bounds are the least conservative in the considered model class. Then, a new multi-rate robust MPC algorithm is developed, employing said multi-step predictors to robustly enforce constraints and stability against disturbances and model uncertainty, and to reduce conservativeness. A simulation example illustrates the effectiveness of the approach.

本笔记扩展了最近提出的算法，用于对受过程和测量干扰影响的渐近稳定、线性时不变系统进行模型识别和鲁棒模型预测控制(MPC)。使用 Set Membership 方法估计不同范围值的独立输出预测变量。结果表明，相应的预测误差界限在所考虑的模型类中是最不保守的。然后，开发了一种新的多速率鲁棒 MPC 算法，采用所述多步预测器来鲁棒地强制执行约束和稳定性以对抗干扰和模型不确定性，并降低保守性。仿真示例说明了该方法的有效性。