Journal
IEEE TRANSACTIONS ON AUTOMATIC CONTROL
Volume 68, Issue 6, Pages 3822-3829Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TAC.2022.3200956
Keywords
Uncertainty; Predictive control; Trajectory; Costs; Uncertain systems; Perturbation methods; Optimal control; Elimination lemma; linear matrix inequalities; robust model predictive control (RMPC); semidefinite relaxation; state-feedback control; uncertain systems
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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. A novel approach is proposed to linearize the nonlinear and nonconvex constrained RMPC problem, with reduced computational burden, through the use of semidefinite relaxation techniques. The effectiveness of the proposed scheme is demonstrated through numerical examples.
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.
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