Title: Synthesise of MPC controller for uncertain systems subject to input and output constraints: application to anthropomorphic robot arm

Authors: Imen Dakhli; Elyes Maherzi; Mongi Besbes

Addresses: Robotics Informatics and Complex Systems LR16ES07, National Engineering School of Tunis, University of Tunis El Manar, BP 37, 1002 Belvedere, Tunisia ' National Engineering School of Carthage, University of Carthage, Tunisia, 2035 Chargia, Tunisia ' Higher Institute of Information and Communication Technologies, University of Carthage Tunisia, BP123, 1164 Hammam Chatt, Tunisia

Abstract: This paper proposes a synthesis of a dynamic controller under constraints. It is based on model predictive control (MPC) approach and resolution of a convex optimisation problem with linear matrix inequalities (LMI). The controller guarantees the closed-loop stability for polytopic time-varying uncertain systems. Conditions are provided for the controller design based on the parameter dependent Lyapunov functions (PDLF). A new demonstration is developed based on the relaxation technique, to include a slack variables G_i. The new LMI's formulation offers an additional degree of freedom for the controller design. Input and output constraints are also taken into account during the design of the controller. This approach allows varying and adjusting the dynamic of system by taking into account input/output constraints.

Keywords: model predictive control; MPC; dynamic controller; linear matrix inequality; LMI; parameter dependent Lyapunov functions; PDLF; input/output constraint.

DOI: 10.1504/IJAAC.2020.103797

International Journal of Automation and Control, 2020 Vol.14 No.1, pp.80 - 97

Received: 29 Jul 2017
Accepted: 07 Mar 2018
Published online: 29 Nov 2019 *

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