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This article presents an extension to the nonlinear model predictive control (MPC) for tracking scheme able to guarantee convergence even in cases of nonconvex output admissible sets. This is achieved by incorporating a convexifying homeomorphism in the optimization problem, allowing it to be solved in the convex space. A novel class of nonconvex sets is also defined for which a systematic procedure to construct a convexifying homeomorphism is provided. This homeomorphism is then embedded in the MPC optimization problem in such a way that the homeomorphism is no longer required in closed form. Finally, the effectiveness of the proposed method is showcased through an illustrative example.

The goal of this note is to highlight that the reformulation of saturation as constraints, typical of the computation of the maximal output admissible sets used in the reference governor literature, is not without loss of generality and may introduce a relevant amount of conservativeness. The note also proposes a modified reference governor able to overcome this limitation.

In this paper, we propose a novel robust model predictive controller for tracking periodic signals for linear systems subject to bounded additive uncertainties based on nominal predictions and constraint tightening. The proposed controller joins optimal periodic trajectory planning and robust control for tracking in a single optimization problem and guarantees that the perturbed closed-loop system converges asymptotically to a neighborhood of an optimal reachable periodic trajectory while robustly satisfying the constraints. In addition, the closed-loop system maintains recursive feasibility even in the presence of sudden changes in the target reference.

In this paper a new model predictive controller for tracking arbitrary periodic references is presented. The proposed controller is based on a single layer that unites dynamic trajectory planning and control. A design procedure to guarantee that the closed loop system converges asymptotically to the optimal admissible periodic trajectory while guaranteeing constraint satisfaction is provided. In addition, the constraints of the optimization problem solved by the controller do not depend on the reference, allowing for sudden changes in the reference without loosing feasibility. The properties of the proposed controller are demonstrated with a simulation example of a ball and plate system. MINECO-Spain and FEDER under project DPI2013-48243-C2-2-R University of Seville under contracts 2014/425 and 2014/758 European Research Council under the European Unions Seventh Framework Programme (FP/2007- 2013)/ ERC Grant Agreement n. 307608

This work proposes a technique for the design of stabilizing dynamic output feedback controllers for discrete-time linear systems with rate and amplitude saturating actuators. The nonlinear effects introduced by the saturations in the closed-loop system are taken into account by using a generalized sector condition, which leads to theoretical conditions for solving the problem directly in the form of linear matrix inequalities.

The usual way to guarantee stability of model predictive control (MPC) strategies is based on a terminal cost function and a terminal constraint region. This note analyzes the stability of MPC when the terminal constraint is removed. This is particularly interesting when the system is unconstrained on the state. In this case, the computational burden of the optimization problem does not have to be increased by introducing terminal state constraints due to stabilizing reasons. A region in which the terminal constraint can be removed from the optimization problem is characterized depending on some of the design parameters of MPC. This region is a domain of attraction of the MPC without terminal constraint. Based on this result, it is proved that weighting the terminal cost, this domain of attraction of the MPC controller without terminal constraint is enlarged reaching (practically) the same domain of attraction of the MPC with terminal constraint; moreover, a practical procedure to calculate the stabilizing weighting factor for a given initial state is shown. Finally, these results are extended to the case of suboptimal solutions and an asymptotically stabilizing suboptimal controller without terminal constraint is presented.

In this note, an efficient way of implementing a constrained min-max predictive controller is presented. The new approach modifies the objective function in such a way that the resulting min-max problem can be solved in polynomial time. Different modifications are proposed. The main contribution of the note is to provide a robust constrained min-max predictive controller that can be implemented in real time. The new controller stabilizes the uncertain system.