Predictive control, which is based on a model of the system to compute the applied input optimizing the future system behavior, is by now widely used. If the nominal models are not given or are very uncertain, data-driven model predictive control approaches can be employed, where the system model or input is directly obtained from past measured trajectories. Using a data informativity framework and Finsler's lemma, we propose a data-driven robust linear matrix inequality-based model predictive control scheme that considers input and state constraints. Using these data, we formulate the problem as a semi-definite optimization problem, whose solution provides the matrix gain for the linear feedback, while the decisive variables are independent of the length of the measurement data. The designed controller stabilizes the closed-loop system asymptotically and guarantees constraint satisfaction. Numerical examples are conducted to illustrate the method.

翻译：预测控制通过系统模型计算最优输入以优化未来系统行为，目前已得到广泛应用。当名义模型未知或高度不确定时，可采用数据驱动模型预测控制方法，直接从历史测量轨迹中获取系统模型或输入。基于数据信息性框架与Finsler引理，我们提出了一种考虑输入和状态约束的、基于线性矩阵不等式的数据驱动鲁棒模型预测控制方案。利用这些数据，我们将问题表述为半定优化问题，其解提供线性反馈的矩阵增益，同时决策变量与测量数据长度无关。所设计的控制器能够渐近镇定闭环系统并保证约束满足性。通过数值算例验证了该方法的有效性。