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Robust constrained model predictive control using linear matrix inequalities. (English) Zbl 0897.93023

In this paper an approach is presented to overcome the main disadvantage of current design techniques for model predictive control (MPC), i.e. their inability to deal explicitly with plant model uncertainty. Hence, the authors present – what is best characterized by the following from their abstract – ‘an approach for MPC synthesis that allows for explicit incorporation of the description of plant uncertainty in the problem formulation. The goal is to design, at each time step, a state-feedback control law that minimizes a worst-case infinite horizon objective function, subject to constraints on the control input and plant output. Using standard techniques $\cdots$ this problem is reduced to a convex optimization involving linear matrix inequalities.’

The authors show that this design results in a control that robustly stabilizes the set of uncertain plants. Several extensions are discussed and well-chosen examples illustrate the theoretical results of this well readable paper which is of interest for control engineers and applied mathematicians interested in automatic control.

Reviewer: I.Troch (Wien)

##### MSC:
 93B51 Design techniques in systems theory 15A39 Linear inequalities of matrices 93D21 Adaptive or robust stabilization
##### Software:
LMI toolbox; LMI Control Toolbox