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An efficient off-line formulation of robust model predictive control using linear matrix inequalities. (English) Zbl 1032.93020
An off-line robust constrained model predictive control (MPC) algorithm for polytopic/norm-bound uncertain linear time-varying state-space systems is derived. The proposed off-line MPC gives a sequence of state feedback matrices corresponding to a sequence of asymptotically stable invariant ellipsoids constructed one inside another in the state space. The sequential implementation of control laws guarantee (optimal) convergence to the origin. Also a continuous feedback function over the state space using the sequence of feedback matrices (which are constant between two adjacent asymptotically stable invariant ellipsoids and discontinuous on the boundary of each invariant ellipsoid) is constructed. It is argued that the on-line MPC computation can be reduced up to three orders of magnitude with little or no loss of performance. Two examples illustrate the implementation of the proposed off-line design.
MSC:
93B51Design techniques in systems theory
93D20Asymptotic stability of control systems
93B40Computational methods in systems theory
15A39Linear inequalities of matrices