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Polytopic Quasi-LPV Approaches for Nonlinear Descriptor Systems: Reduced-Complexity Modeling: Control Design and Application to Robot Manipulators

Abstract : Descriptor systems provide a natural and flexible framework to represent and analyze a large class of engineering applications. Motivated by this fact, this PhD project investigates new quasi-LPV approaches for modeling and control design of descriptor systems with a large number of nonlinearities. The main goal is to derive polytopic quasi-LPV models and the corresponding control design procedures with a numerical reduced-complexity for real-time implementation while paying a special attention on the design conservatism. Although the focused application is related to the control issues of robotic manipulators, with their generic features, the proposed control tools can be also applied to a large class of engineering systems. This manuscript is composed of three main technical parts. For the first part, we introduce the key proprieties and assumptions related to the considered class of nonlinear descriptor systems. We further study the admissibility analysis and the stabilization of nonlinear descriptor systems using Takagi-Sugeno (TS) fuzzy modeling with the well-known sector nonlinearity approach. Based on the initial TS models of nonlinear systems, a complexity-reduction method is proposed to reduce the number of vertices from 2r to r + 1 where r is the number of premise variables. Numerical results are provided to illustrate the design conservatism of this method. For the second part, we develop a new approach to derive an equivalent polytopic representation for a given nonlinear system within a compact set. Although all powerful tools of TS fuzzy framework can be directly applied to the proposed approach, the model complexity only grows proportionally with the number of premise variables, rather than exponentially when compared to the conventional TS fuzzy modeling. Moreover, for the same predefined set of premise variables, the vertices of the proposed polytopic models can admit an infinite number of representations. This non-uniqueness feature allows introducing specific slack variables at the modeling step, which are useful to reduce the control design conservatism. Using the proposed modeling and the descriptor redundancy approach, reduced-complexity admissibility analysis and control design conditions for singular nonlinear systems are derived in terms of linear matrix inequalities (LMIs). Both numerical and physically motivated examples are given to demonstrate the interests of the new control approach with respect to existing TS fuzzy model-based control results. For the third part, using the polytopic quasi-LPV approach proposed in the second part, we develop a new tracking control method for nonlinear descriptor systems with a special focus on manipulator robot applications. The robot systems under algebraic constraints and unmeasured premise variables are transformed into uncertain descriptor polytopic quasi-LPV models for control design. Exploiting the specific structures of robot models, we propose a nonlinear output feedback control scheme for dynamic trajectory tracking, including three key control components: i) feedforward control to account for known disturbances, ii) disturbanceestimation-based control to compensate unknown uncertainties/disturbances, iii) feedback control to guarantee the closed-loop predefined specifications. The control design procedure is recast as a convex optimization under strict LMI constraints, which is a major contribution for output feedback tracking control of nonlinear uncertain descriptor systems. Comparative studies with respect to state-of-the-art tracking control approaches are performed with two manipulators of different natures to demonstrate both theoretical and practical interests of the new approach.
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Contributor : Frédéric Pruvost Connect in order to contact the contributor
Submitted on : Wednesday, September 21, 2022 - 3:05:18 PM
Last modification on : Saturday, September 24, 2022 - 3:58:23 AM


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  • HAL Id : tel-03782774, version 1


Amine Dehak. Polytopic Quasi-LPV Approaches for Nonlinear Descriptor Systems: Reduced-Complexity Modeling: Control Design and Application to Robot Manipulators. Automatic. Université polytechnique Hauts-de-France; Institut national des sciences appliquées Hauts-de-France, 2022. English. ⟨NNT : 2022UPHF0021⟩. ⟨tel-03782774⟩



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