Title: On set-theoretic methods in tracking MPC

Authors: Johannes P. Maree

Addresses: Department of Engineering Cybernetics, Norwegian University of Science and Technology, 7034 Trondheim, Norway

Abstract: The construction of an enlarged terminal constraint set, which consequently implies a larger domain of attraction, is presented for the dual-mode control paradigm for tracking problems. Subsequently, a receding horizon optimal control problem is formulated as a Quadratic Programming problem, which can be efficiently solved on-line. The resulting formulation allows tracking to a set of admissible steady-state/input pairs, thereby, promoting on-line change of economic objectives, by the selection of different operational set-points, whilst, guaranteeing stability and feasibility of the underlying problem. Proof of asymptotic convergence and stability, using Lyapunov arguments, is given for this enlarged set of admissible steady-states.

Keywords: control invariant sets; MPC tracking; Lyapunov; optimal control; quadratic programming; model predictive control; terminal constraint sets; asymptotic convergence; stability; set theory.

DOI: 10.1504/IJSCC.2013.055983

International Journal of Systems, Control and Communications, 2013 Vol.5 No.2, pp.140 - 155

Received: 11 Apr 2013
Accepted: 01 May 2013

Published online: 12 Jul 2014 *

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