Time Optimal Control of Fuzzy Systems: A Parametric Programming Approach

M. Kvasnica, M. Herceg, L. Čirka, and M. Fikar (Slovakia)


Takagi-Sugeno systems, piecewise affine system, explicitmodel predictive control, time-optimal control


This paper presents a novel approach to synthesis of Model Predictive Control laws for the class of models described by Takagi-Sugeno (TS) fuzzy systems. The idea is based on over-approximating the given TS system by a Piecewise Affine (PWA) system and subsequently using PWA-based techniques to synthesize the control policy. PWA systems are similar in nature to the description of TS models in the sense that both classes of models are comprised of several local linear models that are valid over certain regions of the state space. The only difference is that while in the TS model such regions of validity can overlap, in PWA systems they are strictly separated. In order to cope with the overlapping part in establishing relation between TS and PWA models, we consider a class of PWA systems with parametric uncertainties. The proposed approach can guarantee stability of the closed-loop system with the original TS model and can be implemented with very fast sampling rates.

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