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

Bemporad, Alberto and Borrelli, Francesco and Morari, Manfred Min-max control of constrained uncertain discrete-time linear systems. IEEE Transactions on Automatic Control , 48 (9). pp. 1600-1606. ISSN 0018-9286 (2003)

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## Abstract

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.

Item Type: Article 10.1109/TAC.2003.816984 additive norm-bounded input disturbances; constrained uncertain discrete-time linear systems; constraints; continuous piecewise affine function; finite-horizon robust optimal control law; min-max control formulation; multiparametric linear programs; optimal control law; polyhedral parametric uncertainties; receding horizon scheme; robust optimal feedback controller; robustness; state feedback controllers; state vector; state-space matrices; constraint theory; control system synthesis; discrete time systems; linear programming; linear systems; minimax techniques; minimisation; optimal control; piecewise constant techniques; robust control; state feedback; state-space methods; uncertain systems Q Science > QA Mathematics > QA75 Electronic computers. Computer scienceT Technology > TJ Mechanical engineering and machinery Computer Science and Applications Professor Alberto Bemporad 27 Jul 2011 09:02 04 Aug 2011 07:29 http://eprints.imtlucca.it/id/eprint/472