Model Predictive Control by Basil Kouvaritakis & Mark Cannon

Author:Basil Kouvaritakis & Mark Cannon
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(5.5)

with polytopic uncertainty descriptions,

(5.6a)

(5.6b)

where the vertices and , , are assumed to be known. As in earlier chapters, the nominal value of the additive disturbance is taken to be zero.

5.2 Linear Matrix Inequalities in Robust MPC

Linear matrix inequalities were encountered in earlier chapters in the context of ellipsoidal constraint approximations (Sects. 2.​7 and 2.​9) and worst -case quadratic performance indices (Sects. 3.​4 and 4.​2). We begin this section by considering analogous LMI conditions that ensure constraint satisfaction and performance bounds for systems subject to multiplicative model uncertainty. The simplest setting for this is the robust MPC strategy of [8], in which the predicted control trajectories are generated by a linear feedback law:

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