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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 an extension to the existing Model Predictive Control scheme for tracking. This extension is able to provide a solution for the case where the set of steady-state admissible outputs is non-convex. This is achieved by means of a transformation that maps the output set into a convex set. In the proposed scheme, the cost function and constraints of the usual tracking MPC are modified, so that the controller can drive the system to any point in the admissible steady-state domain without violating any constraints. The paper discusses the feasibility and stability of the proposed approach and a final simulation demonstrates the effectiveness of the approach.

Article number 109614 The goal of this paper is to present a systematic method to compute reference dependent positively in- variant sets for systems subject to constraints. To this end, we first characterize these sets as level sets of reference dependent Lyapunov functions. Based on this characterization and using Sum of Squares theory, we provide a polynomial certificate for the existence of such sets. Subsequently, through some algebraic manipulations, we express this certificate in terms of a Semi-Definite Programming problem which maximizes the size of the resulting reference dependent invariant sets. We then present some results implementing the proposed method to an example and propose some variants that may help in reducing possible numerical issues. Finally, the proposed approach is employed in the Model Predictive Control for Tracking scheme to compute the terminal set, and in the Explicit Reference Governor framework to compute the so-called Dynamic Safety Margin. The effectiveness of the proposed method in each of the schemes is demonstrated through simulation studies. Ministerio de Economía y Competitividad de España DPI2016-76493-C3-1-R Ministerio de Ciencia e Innovación (España) PID2019-106212RB-C41