MPC for Tracking of Piece-Wise Constant References for Constrained Linear Systems

MPC for tracking periodic reference signals

“…In effect, the enlargement of the domain of attraction of the proposed controller is more significant since the domain of attraction is the set of states that can reach in N steps any periodic reachable signal of the system. Since a constant reference is a possible periodic reachable signal, the domain of attraction of the proposed controller is larger than the one presented in [Limon et al, 2008], but at expense of a larger number of decision variables.…”

“…(ii) As it was illustrated in [Limon et al, 2008], the addition of the artificial reference in the MPC formulation leads to an enlargement of the domain of attraction of the predictive controller. This property can be extended to the presented controller, but enhanced.…”

“…This problem is analyzed for constrained linear systems and, based on the ideas of [Limon et al, 2008], a novel MPC controller is proposed. As in [Limon et al, 2008], an artificial reachable reference is considered as decision variable as well as the predicted input of the system, a cost function that penalizes the tracking error between the predicted trajectory and the artificial reference is considered, an extended terminal constraint is added and a term penalizing the deviation between the artificial reference trajectory and the known future reference is also added. The proposed controller ensures an admissible evolution for any possible reference and asymptotic stability to the best reachable reference.…”

“…In [Limon et al, 2008 an MPC for tracking constant references is proposed, which is able to lead the system to any admissible set point in an admissible way. The main characteristics of this controller are: an ⋆ This work has been funded by the National Plan Projects DPI2008-05818 and DPI2010-21589-C05-01 of the Spanish Ministry of Science and Innovation and FEDER funds. artificial steady state is considered as a decision variable, a cost that penalizes the error with the artificial steady state is minimized, an additional term that penalizes the deviation between the artificial steady state and the target steady state is added to the cost function (the so-called offset cost function) and an invariant set for tracking is considered as extended terminal constraint.…”

“…It is also assumed that the reference signal is a priori known by the controller. Inspired in the hierarchical control scheme based on the trajectory planification, the ideas of the MPC for tracking [Limon et al, 2008] are extended to this case. The proposed predictive controller has the future sequence of inputs and an artificial reference as decision variables.…”