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A polynomial Linear quadratic Gaussian method is used to compute a controller which is mixed with feedback linearization to control altogether a non linear Quadrotor UAV. A dual criterion involving the minimization of the error and control signal variances is analyzed. The introduction of the feedback linearization is seen to be useful to transform the MIMO system into a non interacting one. This will facilitate the computation of spectral factorization where the behavior is like SISO system. An algorithm is developed in this context. A sliding mode observer is added to feedback loop to estimate the unmeasured states necessary to the inner loop controller. The convergence of output state vector is obtained despite the non-robustness exact linearization when uncertainties on system parameters and disturbances occur. However the sensitivity and complementary sensitivity are presented to confirm the performance and robustness theory and validate the efficiency of results. The weighting functions choice is analyzed through frequency domain. The whole observer-estimator-control constitutes an original suggestion of control system with minimum sensors used. The robustness study has been realized on simulation taking into account uncertainties, disturbances, with a corrupted measured state by noise, and the actuator saturation. The results obtained show the convergence in finite time of estimated values and a satisfying tracking error of desired trajectories.

Polynomial Linear Quadratic Gaussian and Sliding Mode Observer for a Quadrotor Unmanned Aerial Vehicle