Computationally Efficient Robust Model Predictive Control for Uncertain System Using Causal State-Feedback Parameterization

• Published in: IEEE transactions on automatic control Vol. 68; no. 6; pp. 3822 - 3829
• Main Authors: Georgiou, Anastasis, Tahir, Furqan, Jaimoukha, Imad M., Evangelou, Simos A.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.06.2023; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Costs; Discrete time systems; Elimination lemma; Linear matrix inequalities; Mathematical analysis; Optimal control; Optimization; Parameterization; Perturbation; Perturbation methods; Predictive control; Robust control; robust model predictive control (RMPC); semidefinite relaxation; State feedback; state-feedback control; Tracking control; Trajectory; Uncertain systems; Uncertainty
• ISSN: 0018-9286; 1558-2523
• DOI: 10.1109/TAC.2022.3200956

This article investigates the problem of robust model predictive control (RMPC) of linear-time-invariant discrete-time systems subject to structured uncertainty and bounded disturbances. Typically, the constrained RMPC problem with state-feedback parameterizations is nonlinear (and nonconvex) with a prohibitively high computational burden for online implementation. To remedy this, a novel approach is proposed to linearize the state-feedback RMPC problem, with minimal conservatism, through the use of semidefinite relaxation techniques. The proposed algorithm computes the state-feedback gain and perturbation online by solving a linear matrix inequality optimization that, in comparison to other schemes in the literature is shown to have a substantially reduced computational burden without adversely affecting the tracking performance of the controller. Additionally, an offline strategy that provides initial feasibility on the RMPC problem is presented. The effectiveness of the proposed scheme is demonstrated through numerical examples from the literature.