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Robust Model Predictive Control: Piecewise Linear Explicit Solution


A. Bemporad, F. Borrelli, M. Morari

European Control Conference (ECC), Porto, Portugal, pp. 939-944

For discrete-time linear time-invariant systems with input disturbances and constraints on inputs and states, we develop an algorithm to determine explicitly, as a function of the initial state, the solution to robust optimal control problems based on min-max optimization. We show that the optimal control sequence is a piecewise linear function of the initial state. Thus, when the optimal control problem is solved at each time step according to a moving horizon scheme, the on-line computation of the resulting MPC controller is reduced to a simple linear function evaluation. In this paper the uncertainty is modeled as an additive norm-bounded input disturbance vector. The technique can be also extended to robust control of constrained systems affected by polyhedral parametric uncertainty.


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% Autogenerated BibTeX entry
@InProceedings { BemBor:2001:IFA_857,
    author={A. Bemporad and F. Borrelli and M. Morari},
    title={{Robust Model Predictive Control: Piecewise Linear Explicit
    booktitle={European Control Conference (ECC)},
    address={Porto, Portugal},
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