Robust Data-Driven Model Predictive Control With Soft Constrained Strategy
提出一种鲁棒数据驱动模型预测控制方法，通过核函数构建预测模型并用软间隔迭代二次规划更新参数，同时设计双松弛变量的软约束策略处理扰动和异常值，在非线性系统和污水处理仿真中验证了控制性能与鲁棒性的提升。
A robust data-driven model predictive control (RDD-MPC) with a soft constrained strategy is proposed in this article. This method is designed to address model predictive control (MPC) constraint violations caused by external disturbances and outliers arising from measurement errors. First, a robust data-driven prediction model is constructed using kernel functions, and its parameters are updated via the soft-margin-based iterative quadratic programming (SMIQP) algorithm. This algorithm introduces a model slack variable (MSV) to tolerate the negative effects of outliers. This algorithm improves the robustness of the prediction model against outliers and ensures that the model can capture the complex dynamic characteristics of the system. Second, an enhanced soft constrained method (SCM) is designed to handle constraint violations. Unlike SCMs with a single slack variable, which may lead to excessive or insufficient constraint relaxation, this method employs two controller slack variables (CSVs) for coordinated constraint relaxation, thereby ensuring optimization feasibility. Combined with an adaptive weight penalty term, the proposed SCM maintains acceptable control performance in the presence of disturbances. Third, the input-to-state stability (ISS) of the proposed RDD-MPC method is rigorously proven. Finally, experimental results on classic nonlinear systems demonstrate that the proposed method can effectively improve both control performance and robustness. In addition, this method is evaluated on the Benchmark Simulation Model No. 1 (BSM1) for wastewater treatment processes (WWTPs). The experimental results further validate the effectiveness of the RDD-MPC method for systems engineering applications.