Robust GPC-QFT approach using Linear Matrix Inequalities

As well-known in the Model Predictive Control (MPC) community there is a need for looking computationally affordable robust predictive control algorithms that are suitable for on-line implementation. A new control approach mixing Generalized Predictive Control (GPC) and Qualitative Feedback Theory (QFT) is presented for controlling a family of linear uncertain plants. A cascade structure is proposed, combining an inner loop containing a QFT controller with an outer loop where a GPC controller provides adequate references for the inner loop considering input saturations. The idea consists in translating a QFT design to state space and then using Linear Matrix Inequalities (LMI) to obtain a state-vector feedback in such a way that the input reference for the inner loop is calculated in order to satisfy robust tracking problems considering input saturations. Therefore, the proposed solution results in solving a set of constraints being formed by several LMI and Bilineal Matrix Inequalities (BMI), where the aim is to regulate to a fixed reference value.