In this work, it is theoretically demonstrated that a quadrotor can track trajectories using a low-cost GPS with signal losses in unpredictable instants. The lack of a continuous altitude output and the signal loss are solved with certain limitations using two-hybrid linear observers. This type of observer is originally employed to compensate for data loss in computer networks. This was possible due to the sufficient conditions for uniform global asymptotic stability theorems of hybrid systems with persistent jumping. This concept is based on a dynamic hybrid system that guarantees a jumping condition with a Lyapunov function constant when the system flows and decreases during jumps. The quadrotor was modeled like a linear time-invariant system. The results are presented using simulations.

This research introduces a physics-based identification technique utilizing genetic algorithms. The primary objective is to derive a parametric matrix, denoted as A, describing the time-invariant linear model governing the longitudinal dynamics of an aircraft. This is achieved by proposing a fitness function based on the properties of the transition matrix and taking advantage of some of the capabilities of the genetic algorithm, mainly those of restricting the search ranges of the unknowns. In this case, such unknowns are related to the type of aircraft and flight conditions that are considered during the identification process. The proposed identification method is validated with a reliable nonlinear model that can be found in the literature, as well as with the calculation of the trim condition and linearization generally used in aircraft dynamics. In summary, this study suggests that the genetic algorithm provided with the adequate fitness function could be an appealing alternative for aircraft model identification, even when limited data are available. Furthermore, in some cases, linearization using a genetic algorithm can be more efficient than classical methods.

The stability of autonomous dynamical switched systems is analyzed by means of multiple Lyapunov functions. The stability theorems given in this paper have finite number of conditions to check. It is shown that linear functions can be used as Lyapunov functions. An example of an exponentially asymptotically stable switched system formed by four unstable systems is also given.

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.

Most works related to the identification of mathematical nonlinear systems suggest that such approaches can always be directly applied to any nonlinear system. This misconception is greatly discouraging when the obtained results are not expected. Thus, the current work hypothesizes that the more information one has about the mathematical structure of the model, the most precise the identification result. Therefore, a variant of the Sparse Identification of Nonlinear Dynamics (SINDY) approach is presented to obtain the full mathematical nonlinear model of a high-order system with coupled dynamics, namely, a commercial quadcopter. Furthermore, due to its high sensitivity to inputs, a control system is devised using the identified model to stabilize the quadcopter. This illustrates the effectiveness of the proposed identification method.

In this paper, a modification of the classical PID controller scheme for position control is presented. The resulting controller incorporates an exponential trajectory that smoothly guides the system towards the setpoint and a hybrid mechanism to dynamically reset the exponential signal, allowing an adaptive response to discontinuous reference signals. This combination leverages the benefits of exponential trajectories to reduce overshoot and transient oscillations, while the hybrid system ensures robust performance over a wide range of operating scenarios. Among the advantages of the proposed approach, two stand out: (1) significant improvements in energy savings can be achieved in some cases, and (2) closed-loop system performance can be improved even considering poorly tuned PIDs.