Stable IHMPC for Unstable Systems

• Published in: IFAC Proceedings Volumes Vol. 41; no. 2; pp. 6950 - 6955
• Main Authors: González, Alejandro H., Sotomayor, Oscar A.Z., Odloak, Darci
• Format: Journal Article
• Language: English
• Published: 2008
• ISSN: 1474-6670
• DOI: 10.3182/20080706-5-KR-1001.01178

An alternative method to formulate the stable Model Predictive Control (MPC) optimization problem, which allows controlling unstable systems with a large domain of attraction, is presented in this work. Usually, stability is guaranteed by means of an appropriate selection of a terminal cost, a terminal constraint, and a local unconstrained controller for predictions beyond the control horizon. This is the case, for instance, of the infinite horizon MPC (IHMPC) with a null local controller, and the dual MPC with a local Linear Quadratic Regulator (LQR). In the last case, the MPC formulation also allows a local optimality. However, its domain of attraction is limited (small, in most of the cases) and depends on the size of the terminal set and the length of the control horizon. Here we propose the inclusion of an appropriate set of slacked terminal constraints into the optimization problem as a way to enlarge the domain of attraction of the MPC that uses the null local controller. In addition, this slack allows a simple offset-free operation in the proximities of the input saturation. Despite the proposed controller does not achieve local optimality, simulations show that its performance is similar to the one obtained with the dual MPC that uses a LQR local controller.