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Decomposition principle in model predictive control for linear systems with bounded disturbances. (English) Zbl 1185.93024
Summary: Considering a constrained linear system with bounded disturbances, this paper proposes a novel approach which aims at enlarging the domain of attraction by combining a set-based Model Predictive Control (MPC) approach with a decomposition principle. The idea of the paper is to extend the “pre-stabilizing” MPC, where the MPC control sequence is parameterized as perturbation to a given pre-stabilizing feedback gain, to the case where the pre-stabilizing feedback law is given as the linear combination of a set of feedback gains. This procedure leads to a relatively large terminal set and consequently a large domain of attraction even when using short prediction horizons. As time evolves, by minimizing the nominal performance index, the resulting controller reaches the desired optimal controller with a good asymptotic performance. Compared to the standard “pre-stabilizing” MPC, it combines the advantages of having a flexible choice of feedback gains, a large domain of attraction and a good asymptotic behavior.
MSC:
93B11System structure simplification
93B40Computational methods in systems theory
93C05Linear control systems
93C73Perturbations in control systems