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. (shrink)

In this research, a sliding mode regulator with sine mapping is suggested for the stabilization of electricity generators being affected by magnet interaction nonlinearities and generator nonlinearities. To reach this goal, our suggested regulator has the following contributions: it starts from the sliding mode regulator with the modifications that the saturation mapping is used to reach a smoother performance instead of the signum mapping, and the sine mapping is applied to reach an upper bound in the proportional gain error, it (...) is used to reach some chosen constant behaviors for the angle position, angle speed, and current in the electricity generators, and its stabilization is ensured based on the Lyapunov approach. We show the simulation of the suggested regulator in two electricity generators. (shrink)