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The aim of this work is to apply an innovative adaptive ℒ1 techniques to control flutter phenomena affecting highly flexible wings and to evaluate the efficiency of this control algorithm and architecture by performing the following tasks: i) adaptation and analysis of an existing simplified nonlinear plunging/pitching 2D aeroelastic model accounting for structural nonlinearities and a quasi-steady aerodynamics capable of describing flutter and post-flutter limit cycle oscillations, ii) implement the ℒ1 adaptive control on the developed aeroelastic system to perform initial control testing and evaluate the sensitivity to system parameters, and iii) perform model validation and calibration by comparing the performance of the proposed control strategy with an adaptive back-stepping algorithm. The effectiveness and robustness of the ℒ1 adaptive control in flutter and post-flutter suppression is demonstrated.