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In this note, the problem of tracking random references and rejecting random perturbations in a quadrotor, both generated by an auxiliary system named exosystem, is solved by extending the deterministic tracking problem to the area of stochastic processes. Besides, it is considered that only a part of the state vector of the quadrotor is available through measurements. As a consequence, the state vector of the plant must be estimated in order to close the control loop. On this basis, a controller to track random references and to reject random perturbations is developed by combining a Kalman filter to estimate the references and perturbations of an exosystem and an observer to estimate the states of a quadrotor. Besides, to obtain a more practical controller, the analysis is carried out in discrete time. Numerical simulations are used in a quadrotor to confirm the validity and effectiveness of the proposed control.

On the Rejection of Random Perturbations and the Tracking of Random References in a Quadrotor