This paper presents a full degrees-of-freedom (DOFs) robust control design for a nonlinear quadrotor unmanned aerial vehicle (UAV) operating under bounded disturbances. Second-order sliding modes controllers (SOSMCs) are designed so that the quadrotor UAV can follow a 3D trajectory in the presence of model uncertainties, underactuation, as well as external disturbances that may be matched or mismatched, and vanishing or nonvanishing. The stability analysis of the closed-loop system is presented via the Lyapunov method, showing the finite-time convergence of the system trajectories to the sliding surfaces, as well as the finite-time convergence of the quadrotor position and attitude to their reference values. The high-gain adaptation (HGA) method is adopted in the SOSMC technique, called SOSMC-HGA, to alleviate the chattering phenomenon. Simulation studies in different scenarios demonstrate that the SOSMC technique exhibits superior tracking performance and robustness properties compared to concurrent control methods for tracking reference trajectories of quadrotor UAVs. The simulation results confirm that SOSMC-HGA significantly attenuates the chattering phenomenon in control signals and system states, which is an important improvement, as it increases the safety of UAVs and reduces power consumption.

This paper introduces a novel approach for state-space representation of linear time invariant (LTI) systems, so-called Future Inputs Elimination (FIE) method. It can be applied to single-input-single-output (SISO) or multiple-input-multiple-output (MIMO) systems, continuous-time or discrete-time systems, whose dynamic equations are coupled or separated (uncoupled) in terms of their inputs and outputs. The FIE method closely parallels to the controllable canonical method when restricted to a class of SISO LTI systems. Moreover, it retains an easy implementation and effortless computation even for a class of MIMO LTI systems. The proposed approach may be used for representation of LTI systems with multiple or complex-conjugate poles. Many representative numerical examples are provided in order to illustrate the effectiveness of the elimination state-space method for representation of both SISO and MIMO LTI systems.

Control design for multi-rotor aerial vehicles (MAVs) is quite challenging problem due to their nonlinearitles, unknown dynamics, parametric uncertainties, an underactuated property, a nonlinear coupling dynamics and external disturbances. This paper introduces a first order sliding mode control (FOSMC) for robust stabilization of an under-actuated quad-rotor unmanned aerial vehicle (UAV) operating in the presence of external disturbances. The proposed FOSMC guarantees a finite time convergence of the system trajectories to the sliding surface. Obtained simulations show that the FOSM based approach improves robustness properties compared with the concurrent techniques, and enhance tracking performance of the quad-rotor UAV exposed to external disturbances.