Asymmetric constraints with polytopic sets in MPC with application to coupled tanks system

Abstract

SUMMARYAsymmetric constraints have not received sufficient attention in the MPC literature, possibly due to the popularity of ellipsoidal terminal regions, which for asymmetric constraints would give conservative results. The work here adopts low-complexity polyhedra for which invariance and feasibility under asymmetric constraints can be handled through the use of Farkas' lemma and related results. The paper embeds these results into an MPC law based on a dual mode prediction strategy and proposes algorithms for the systematic design of the polytopic terminal sets. The efficacy of the results is illustrated through application to a coupled tanks system.

Constrained Uncertain System Stabilization with Enlargement of Invariant Sets

“…Relations (21)-(23) imply the positive invariance and attractivity of S i ′ , while (24) and (25) guarantee constraint satisfaction.…”

“…e computation of the maximal controlled invariant set process introduced in [21] and the corresponding state feedback control laws for linear systems subject to polyhedral input and state constraints have been studied in [22,23]. Kouvaritakis et al [24] developed an advanced method to enlarge the terminal invariant set using a linear programming approach. In the study by Henrion et al [25], convex optimization problems are formulated for the region enlargement and hence tuning parameters for the positively invariant set improvement.…”

A novel approach to the computation of the maximal controlled invariant set for constrained linear systems

“…In [12] an LMI approach was used for the enlargement of the domain of attraction using lifting techniques. The terminal invariant set in [13] was enlarged using a linear programming approach. In [14] convex optimization problems are formulated for the enlargement of the stability region.…”