Further Results on the Exploration of Combinatorial Tree in Multi-Parametric Quadratic Programming

Parisa Ahmadi-Moshkenani 1 Sorin Olaru 2, 3 Tor Johansen 1
2 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 : — A combinatorial approach has been recently proposed for multi-parametric quadratic programming and has shown to be more effective in finding the complete solution than existing geometric methods for higher-order systems. In this paper, we propose a method for exploring the combinatorial tree which exploits some of the underlying geometric properties of adjacent critical regions as the supplementary information in combinatorial approach to exclude a noticeable number of feasible candidate active sets from combinatorial tree. This method is particularly well-suited for cases where many combinations of active constraints are feasible but not optimal. Results indicate that this method can find all critical regions corresponding to non-degenerate multi-parametric programming. A post-processing algorithm can be applied to complete the proposed method in the cases in which some critical regions might not be enumerated due to degeneracies in the problem.
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Parisa Ahmadi-Moshkenani, Sorin Olaru, Tor Johansen. Further Results on the Exploration of Combinatorial Tree in Multi-Parametric Quadratic Programming. 15th European Control Conference (ECC 2016), Jun 2016, Aalborg, Denmark. ⟨10.1109/ecc.2016.7810273⟩. ⟨hal-01429237⟩

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