Control of linear systems with non-convex constraints. Mixed integer formulations, MPC design and interpolation alternatives

Sorin Olaru 1, 2
1 DISCO - Dynamical Interconnected Systems in COmplex Environments
L2S - Laboratoire des signaux et systèmes, Inria Saclay - Ile de France, SUPELEC, CNRS - Centre National de la Recherche Scientifique : UMR8506
Abstract : The paper deals with the control of linear discrete-time systems in presence of non-convex state-space constraints, understood as obstacles for the closed-loop trajectories. These interdicted regions can include the origin and as a consequence, the natural limit behavior has to be replaced by a new admissible equilibrium point, possibly by activating a subset of constraints. It will be shown that a predictive control strategy can deal, by its generic formulation, with such problems and several refinements will be pointed out with respect to the dual-mode principles and the numerical formulations of the optimization problems. Furthermore, the second goal of the paper is to present an interpolation-based procedure as a reduced-complexity alternative to the classical receding horizon optimization. The basic elements for the establishment of such a control scheme are the boundary of the closed convex sets in the state-space and the associated vertex controller.
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Conference papers
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https://hal-supelec.archives-ouvertes.fr/hal-00751460
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Submitted on : Tuesday, November 13, 2012 - 2:49:25 PM
Last modification on : Saturday, September 15, 2018 - 1:03:07 AM

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Sorin Olaru. Control of linear systems with non-convex constraints. Mixed integer formulations, MPC design and interpolation alternatives. 4th IFAC Nonlinear Model Predictive Control Conference, Aug 2012, Noordwijkerhout, Netherlands. pp.392-399, ⟨10.3182/20120823-5-NL-3013.00090⟩. ⟨hal-00751460⟩

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