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Min-max control of constrained uncertain discrete-time linear systems

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3 Author(s)
A. Bemporad ; Dipt. Ingegneria dell'Informazione, Univ. di Siena, Italy ; F. Borrelli ; M. Morari

For discrete-time uncertain linear systems with constraints on inputs and states, we develop an approach to determine state feedback controllers based on a min-max control formulation. Robustness is achieved against additive norm-bounded input disturbances and/or polyhedral parametric uncertainties in the state-space matrices. We show that the finite-horizon robust optimal control law is a continuous piecewise affine function of the state vector and can be calculated by solving a sequence of multiparametric linear programs. When the optimal control law is implemented in a receding horizon scheme, only a piecewise affine function needs to be evaluated on line at each time step. The technique computes the robust optimal feedback controller for a rather general class of systems with modest computational effort without needing to resort to gridding of the state-space.

Published in:

IEEE Transactions on Automatic Control  (Volume:48 ,  Issue: 9 )