Contribution à l’estimation d’état des systèmes non linéaires décrits par les multi-modèles flous

Abstract

he research work presented in this thesis focuses on the state estimation of nonlinear systems described by the Takagi-Sugeno multi-model with unmeasurable premise variables. The primary contribution of this work lies in mitigating conservatism in the stability conditions of the state estimation error dynamics. To alleviate this conservatism, the poly-quadratic Lyapunov function was employed, specifically to reduce the conservatism associated with the quadratic approach. Various methodologies have been presented based on this function, encompassing the Lipschitz method, L2-gain synthesis, and the differential mean value theorem. We derived linear and bilinear stability conditions for the convergence of the estimation error dynamics, and we have introduced an efficient algorithm for solving the bilinear one, which was then compared to other existing solvers. In the second part of this work, the challenges of unknown inputs have been addressed. We presented different observer designs, including proportional integral, proportional multi-integral, and decoupled unknown input observers. Furthermore, we tackled the challenge of the real-time applicability of the observer by optimizing the observer’s Lyapunov matrix. This methodology was implemented and tested for unknown input observers in real-time examples, and a comprehensive discussion comparing the performance of the various unknown input observers was provided. Overall, this research contributes to advancing the understanding and practical implementation of state and unknown input estimation techniques in complex nonlinear systems.