GPC Robust Design Using Linear and/or Bilinear Matrix Inequalities*

Abstract

This article proposes an integrated methodology for the robust design of a generalized predictive controller (GPC) based on linear and/or bilinearmatrix inequalities (LMIs/ BMIs). Firstly, a GPC formulation in state space which incorporates a full rank observer to estimate the on-line states is presented. It is then shown that the poles of such an observer are equivalent to the roots of filter polynomials Tj(z−1) in a GPC Input/Output (I/O)formulation, which implies that these poles inherit the robustness effect associated with filter polynomial roots. In this way, we obtain closed-loop robust stability conditions and closedloop robust ∞ -norm bounding conditions for the design of a GPC, based on LMIs and/or BMIs. These conditions take into account linear fractional (LFR) plant uncertainty. This type of uncertainty also contains affine dependence as a particular case, and can represent any matrix rational function. Finally, the robust GPC parameters are optimally obtained using a multiobjective genetic algorithm (GA). This integrated methodology is applied, as an example, to themultiobjectivemaximization of an uncertainty range and ∞ -norm minimization in a benchmark plant: the twomass-spring mechanical system.