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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 paper is to present a nonlinear Model Predictive Control scheme for boom cranes, one of the most common type of rotary cranes. In this paper we first present a complete mathematical model for this type of cranes where it is possible to control the two rotations of the crane and the cable length. Then, we design a Model Predictive Control law able to drive the load to a desired position while fulfilling mechanical and safety constraints. We finally compare our controller to a partial feedback linearization coupled with a proportional derivative control with gravity compensation applied to the same model.

The explicit reference governor (ERG) is an add-on unit that provides constraint handling capabilities to pre-stabilized systems. In particular, the ERG acts on the reference of the pre-stabilized system in such a way that, even for large transients, constraints are satisfied. A standard way to build an ERG is to translate state and input constraints into a constraint on the value of the Lyapunov function associated to the currently applied reference. The main challenge of this approach is the determination of the largest reference-dependent Lyapunov level set that ensures constraint satisfaction. In general, the optimization problem to compute such a level set is non-convex. This letter proposes a novel systematic approach for designing an ERG for linear systems subject to combinations of intersections and unions of concave constraints. More precisely, first, it is shown that the solution of the stated non-convex problem can be approximated by solving multiple convex problems (one convex optimization problem for each constraint) and then suitably combining their solutions. Then, since these convex problems do not admit a closed-form solution, a virtual continuous-time system is proposed to estimate their solutions. Finally, an upper-bound for the estimation error is provided analytically, and a procedure is proposed to increase the robustness of the ERG against estimation errors. The effectiveness of the proposed scheme is demonstrated on a simulated case study.

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

This paper presents the first release of the Explicit Reference Governor Toolbox (ERGT), whichcan be downloaded from the website https://saasofcc.wordpress.com/erg-toolbox/. The ERGT provides a user-friendly interface for the design of an Explicit Reference Governor, which is an add-on unit that provides constraint handling capabilities to closed loop systems. At the present stage, the toolbox can be used to design an ERG for the constrained control of linear systems subject to the union and intersection of linear constraints. The paper describes several ERGT resources, such as i) built-in Matlab functions for the design phase, ii) Simulink blocks for performing simulations, and iii) a simple tutorial of how to use the toolbox. Additionally, this paper extends the ERG scheme to deal with constraints in the form of union of convex polyhedra.