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Computation of robust control invariant sets with predefined complexity for uncertain systems
Author(s) -
Gupta Ankit,
Köroğlu Hakan,
Falcone Paolo
Publication year - 2020
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.5378
Subject(s) - computation , robust control , maximization , invariant (physics) , mathematics , mathematical optimization , piecewise , affine transformation , algorithm , linear matrix inequality , controller (irrigation) , control theory (sociology) , computer science , control system , control (management) , artificial intelligence , mathematical analysis , agronomy , electrical engineering , pure mathematics , engineering , mathematical physics , biology
Abstract This paper presents an algorithm that computes polytopic robust control‐invariant (RCI) sets for rationally parameter‐dependent systems with additive disturbances. By means of novel linear matrix inequalities (LMI) feasibility conditions for invariance along with a newly developed method for volume maximization, an iterative algorithm is proposed for the computation of RCI sets with maximized volumes. The obtained RCI sets are symmetric around the origin by construction and have a user‐defined level of complexity. Unlike many similar approaches, the proposed algorithm directly computes the RCI sets without requiring control inputs to be in a specific feedback form. In fact, a specific control input is obtained from the LMI problem for each extreme point of the RCI set. The outcomes of the proposed algorithm can be used to construct a piecewise‐affine controller based on offline computations.