In this article we present a flatness-based controller that solves the trajectory tracking problem for an unmanned four-rotor aircraft. A simple version of the dynamical system obtained from a suitable coordinate transformation of the Euler–Lagrange model of the system is used. This model, combined with a suitable input saturation nonlinearity, also avoids the inconvenient system singularities. The corresponding tracking error is shown to be globally asymptotically stable but only locally exponentially stable, while the controller maintains the four-rotor system motions inside a feasible region. Numerical simulations are presented to assesses the effectiveness of the proposed control strategy.

We introduce a control strategy to solve the regulation control problem, from the perspective of trajectory planning, for an uncertain 3D overhead crane. The proposed solution was developed based on an adaptive control approach that takes advantage of the passivity properties found in this kind of systems. We use a trajectory planning approach to preserve the accelerations and velocities inside of realistic ranges, to maintaining the payload movements as close as possible to the origin. To this end, we carefully chose a suitable S-curve based on the Bezier spline, which allows us to efficiently handle the load translation problem, considerably reducing the load oscillations. To perform the convergence analysis, we applied the traditional Lyapunov theory, together with Barbalat’s lemma. We assess the effectiveness of our control strategy with convincing numerical simulations.

Departing from analyzing a general input-saturated second-order system, a Lyapunov-based constructive procedure for the output-feedback stabilization of the constantly perturbed DC-DC buck power converter is presented. The proposed scheme also incorporates a Σ-Δ modulator. The obtained control scheme is developed in two parts: a proportional-integral-type family of algorithms devoted to regulating the uncertain system by using measurements of the output voltage and a Σ-Δ modulator dedicated to transforming the control action into a {0, 1} discrete-valued signal. This modulator is a kind of a sliding controller, which can be seen as a subsystem with an on-off output. This combination, the PI-type family of controllers and the Σ-Δ modulator, assures the global stability of the closed-loop system, even if parametric uncertainties are presented. The convergence analysis was carried out using Lyapunov's method. The theoretical results are confirmed using real-time experimental tests, which demonstrate the anti-windup scheme and the Σ-Δ modulator efficiency. The experiments consider the saturation of the control input and disturbances, having obtained convincing results.