This paper addresses the tracking control of quadrotors flying outdoors. Two control laws are combined and tested in real-time experiments. The aircraft attitude and the translational displacement are controlled using the backstepping approach, while the altitude is controlled using the sliding mode control strategy. In both cases, new modifications are introduced with respect to the existing classical algorithms. Concerning the backstepping algorithm, we introduce the dynamical model of the quadrotor in the controller design and this guarantees that the virtual input is bounded. On the other hand, the proposed sliding mode control assures that the vehicle's altitude converges in finite time to the desired reference, even when uncertainties are considered in the system. The proposed controller is tested in an outdoor environment and the experiments highlighted the controllers' reliability. Additionally, the performance of the closed-loop plant with the proposed controllers is compared with the performance given by a proportional-derivative controller.

In this contribution we propose to extend the well-known iterative procedure for the synthesis of suboptimal control laws for linear delay free control system introduced in Vaisbord ( 1963 Vaisbord, EM . 1963. An Approximate Method for the Synthesis of Optimal Control. Automation and Remote Control, 24: 1482–1488. [Google Scholar] ) to the case of control systems with pointwise and distributed delays. The iterative procedure is based on the idea of the approximate construction of the Bellman functional in the form of quadratic Lyapunov–Krasovskii functionals. The procedure at each step generates a new stabilising suboptimal control law that reduces the value of the quadratic performance index. We present in this contribution formulas for the computation of control laws.

A robust control strategy to stabilize a PVTOL aircraft in the presence of crosswind is proposed in this paper. The approach makes use of Robust Control Lyapunov Functions (RCLF) and Sontag's universal stabilizing feedback. A nonlinear dynamic model of the aircraft taking account the crosswind has been developed. Likewise, a robust nonlinear control strategy is proposed to stabilize the PVTOL aircraft using RCLF, and we have employed the Riccati equation's parameters to compute and tune it in real-time. To validate the proposed control strategy, various simulations have been carried out. The controller has been also applied in real-time to a PVTOL prototype undergoing crosswinds. The experimental results show the good performance of the control algorithm.

Robust stability conditions for systems with distributed delays are presented. The result is derived within the approach of Lyapunov-Krasovskii functional of complete type. Here, the prescribed derivative includes general cross terms. As a consequence the robustness margins are less conservative than those obtained in previous contributions