{"corpus_id":149667677,"paper_sha":"b215e75c71b3c851b922a622830d4e7650058025","doi":"10.1002/rnc.4573","arxiv_id":null,"pmid":null,"pmcid":null,"mag_id":2941851444,"dblp_id":null,"acl_id":null,"title":"Full‐complexity polytopic robust control invariant sets for uncertain linear discrete‐time systems","year":2019,"publication_date":"2019-04-23","venue":"International Journal of Robust and Nonlinear Control","journal":{"name":"International Journal of Robust and Nonlinear Control","pages":"3587 - 3605","volume":"29"},"journal_issn":null,"journal_title":null,"publication_types":[],"pubmed_pub_types":null,"s2_fields_of_study":["Computer Science","Engineering"],"reference_count":46,"citation_count":25,"influential_citation_count":2,"is_open_access":true,"arxiv_categories":null,"arxiv_license":null,"arxiv_journal_ref":null,"mesh_headings":null,"chemicals":null,"comments_corrections":null,"source_flags":1,"s2_open_access_pdf_url":"http://spiral.imperial.ac.uk/bitstream/10044/1/71831/2/RCIS_IJRNC_V6.pdf","s2_open_access_landing_url":"https://www.semanticscholar.org/paper/b215e75c71b3c851b922a622830d4e7650058025","s2_open_access_license":null,"s2_open_access_status":"GREEN","pmc_open_access_pdf_url":null,"pmc_open_access_landing_url":null,"pmc_open_access_license":null,"pmc_open_access_status":null,"unpaywall_open_access_pdf_url":null,"unpaywall_open_access_landing_url":null,"unpaywall_open_access_license":null,"unpaywall_open_access_status":null,"abstract":"This paper presents an algorithm for the computation of full‐complexity polytopic robust control invariant (RCI) sets, and the corresponding linear state‐feedback control law. The proposed scheme can be applied for linear discrete‐time systems subject to additive disturbances and structured norm‐bounded or polytopic uncertainties. Output, initial condition, and performance constraints are considered. Arbitrary complexity of the invariant polytope is allowed to enable less conservative inner/outer approximations to the RCI sets whereas the RCI set is assumed to be symmetric around the origin. The nonlinearities associated with the computation of such an RCI set structure are overcome through the application of Farkas' theorem and a corollary of the elimination lemma to obtain an initial polytopic RCI set, which is guaranteed to exist under certain conditions. A Newton‐like update, which is recursively feasible, is then proposed to yield desirable large/small volume RCI sets.","claims":[{"public_id":"cl_0b6e212beddcd3976b85295dfa1ab524","status":"active","text":"A recursively feasible Newton-like update is proposed to produce robust control invariant sets with desirable large or small volume.","confidence":0.9,"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous (12632b8b5f)","roles":["extraction"],"url":"https://sah.borca.ai/u/12632b8b5f"}],"url":"https://sah.borca.ai/claims/cl_0b6e212beddcd3976b85295dfa1ab524"},{"public_id":"cl_954f1bbe1618c6f3692910ea3d2f8516","status":"active","text":"Allowing arbitrary invariant-polytope complexity enables less conservative inner and outer approximations of the robust control invariant set, under the assumption of symmetry around the origin.","confidence":0.93,"contributors":[{"id":1,"public_id":"12632b8b5f","public_label":"Anonymous 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