(188i) Stability Analysis of Model Predictive Control Using Piecewise Affine Models Under Unstructured Uncertainty
Piecewise affine (PWA) models have been widely used in MPC (Bemporad & Morari, 1999), (Rewienski & White, 2003), (Xie et al, 2011)â to adequately describe the nonlinear dynamics using different linear models to span the state domain. In this work, we extend the applicability of IQCs for input/ouput stability analysis to PWA systems. To avoid the expensive computational cost of mixed integer programming while employing online optimisation, one linear model is used for each sampling time. In order to construct the model pool we collect computed trajectories and linearization is applied at selected transient points. Furthermore, even though the constructed PWA models approximate complex dynamics efficiently, uncertainties may still arise. IQCs can describe the input/output behaviour of nonlinear and uncertain components in the closed loop. Therefore all possible troublemaking parts can be considered assuming that they satisfy IQCs. Then dissipation inequalities can include IQCs to analyse input/output stability. Additionally, the constructed controller selects which model will be used every sampling time. Therefore changes from model to model may destabilise theÂ system. Our analysis is able to guarantee that the closed loop system will remain stable. The proposed methodology is demonstrated through two chemical engineering case studies.
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