Full‐complexity polytopic robust control invariant sets for uncertain linear discrete‐time systems

Liu, Chengyuan; Tahir, Furqan; Jaimoukha, Imad M.

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.

Citation

Liu, C., Tahir, F., & Jaimoukha, I. M. (2019). Full‐complexity polytopic robust control invariant sets for uncertain linear discrete‐time systems. International Journal of Robust and Nonlinear Control, 29(11), 3587-3605. https://doi.org/10.1002/rnc.4573

• Journal Article Type: Article
• Acceptance Date: Apr 1, 2019
• Online Publication Date: Apr 23, 2019
• Publication Date: Jul 25, 2019
• Deposit Date: May 14, 2019
• Publicly Available Date: Apr 24, 2020
• Journal: International Journal of Robust and Nonlinear Control
• Print ISSN: 1049-8923
• Electronic ISSN: 1099-1239
• Publisher: Wiley
• Peer Reviewed: Peer Reviewed
• Volume: 29
• Issue: 11
• Pages: 3587-3605
• DOI: https://doi.org/10.1002/rnc.4573
• Public URL: https://nottingham-repository.worktribe.com/output/2052706
• Publisher URL: https://onlinelibrary.wiley.com/doi/full/10.1002/rnc.4573
• Additional Information: This is the peer reviewed version of the following article: iu, C, Tahir, F, Jaimoukha, IM. Full‐complexity polytopic robust control invariant sets for uncertain linear discrete‐time systems. Int J Robust Nonlinear Control. 2019; 1– 19, which has been published in final form at https://doi.org/10.1002/rnc.4573. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.