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Computation of Invariant Tubes for Robust Output Feedback Model Predictive Control

Hu, Cheng; Liu, Chengyuan; Jaimoukha, Imad M

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Authors

Cheng Hu

Chengyuan Liu

Imad M Jaimoukha



Abstract

This paper presents an algorithm to calculate tightened invariant tubes for output feedback model predictive controllers (MPC). We consider discrete-time linear time-invariant (DLTI) systems with bounded state and input constraints and subject to bounded disturbances. In contrast to existing approaches which either use pre-defined control and observer gains or compute the control and observer gains that optimize the volume of the invariant sets for the estimation and control errors separately, we consider the problem of optimizing the volume of these sets simultaneously. The nonlinearities associated with computing the control and observer gains are circumvented by the application of Farkas' Theorem and an extended Elimination Lemma, to convert the nonconvex optimization problem into a convex semidefinite program. An update algorithm is then used to reduce the volume of the invariant tube through a finite number of iterations. Numerical examples are provided to illustrate the effectiveness of the proposed algorithm.

Citation

Hu, C., Liu, C., & Jaimoukha, I. M. (2020). Computation of Invariant Tubes for Robust Output Feedback Model Predictive Control

Conference Name 21st IFAC World Congress
Start Date Jul 12, 2020
End Date Jul 17, 2020
Acceptance Date Feb 27, 2020
Publication Date Jul 11, 2020
Deposit Date Feb 27, 2020
Publicly Available Date Mar 29, 2024
Keywords Robust control invariant sets; linear matrix inequality; robust model predictive control; uncertain linear systems; optimization
Public URL https://nottingham-repository.worktribe.com/output/4044422
Related Public URLs https://www.ifac2020.org/

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