This paper presents a systematic procedure for the control scheme design for a PVTOL aircraft system with an inverted pendular load, which is a nonlinear underactuated system. The control scheme is based on the use of angular movement as an artificial control in order to propose new auxiliary control inputs. This is achieved by a linear extended state observer-based active disturbance rejection control to reject both nonmodeled dynamics and external disturbances. The flying planar inverted pendulum is then linearized around an unstable equilibrium point, and the resulting system is subdivided into two subsystems: (1) the height system, and (2) the horizontal pendulum system. For the height system, a linear extended state observer-based active disturbance rejection control is proposed in order to accomplish a take-off and landing task in the presence of external disturbances and non-linearities neglected in the linearization process. The flatness property in the horizontal-pendulum system is exploited in order to propose another active disturbance rejection control of linear nature. The flatness of the tangentially linearized model provides a unique structural property that results in an advantageous low-order cascade decomposition of the linear extended state observer design. Numerical simulations show the effectiveness of the proposed control scheme in trajectory tracking tasks in the presence of disturbances caused by crosswinds with random amplitudes.

This paper presents a control scheme that allows height position regulation and stabilization for an unmanned planar vertical takeoff and landing aircraft system with an inverted pendular load. The proposed controller consists of nested saturations and a generalized proportional integral (GPI). The GPI controls the aircraft height and the roll attitude; the latter is used as the fictitious input control. Next, the system is reduced through linear transformations, expressing it as an integrator chain with a nonlinear perturbation. Finally, the nested saturation function-based controller stabilizes the aircraft’s horizontal position and the pendulum’s angle. Obtaining the control approach was a challenging task due to the underactuated nature of the aircraft, particularly ensuring the pendulum’s upright position. The stability analysis was based on the second method of Lyapunov using a simple candidate function. The numerical simulation confirmed the control strategy’s effectiveness and performance. Additionally, the numerical simulation included a comparison against a PD controller, where its corresponding performance indexes were estimated, revealing that our controller had a better response in the presence of unknown disturbances.

This work proposes an Adaptive Neural Control for the asymptotic stabilization of a chain of integrators at the origin. The proposed approach addresses the stabilization of the integrator chain by means of a control law whose applied signal is structurally bounded to $(-1,1)$ by the hyperbolic tangent architecture, i.e., $u\left(t\right)=tanh\left(z\right)$, where z represents a weighted linear combination of the system states and a bias term. Furthermore, an adaptation law for the weights is proposed, based on the classical backpropagation algorithm for neural networks. The stability analysis is conducted using singular perturbation theory, demonstrating that, under a sufficiently high learning rate, the closed-loop system exhibits a Standard Singular Perturbation Form. This formulation allows for the analysis of the system across two distinct time scales: the adaptation dynamics (fast subsystem) and the state dynamics (slow subsystem). Based on this formulation, explicit conditions on the learning rate and the initial conditions are derived to guarantee local asymptotic stability using Tikhonov’s theorem. These conditions characterize the region of attraction and ensure that the adaptive neural controller stabilizes the system. Numerical simulations were carried out to evaluate the controller’s performance under three different scenarios: ideal conditions, initialization outside the region of attraction, and a low learning rate. These scenarios illustrate the closed-loop system behavior and validate the theoretical conditions required for asymptotic stability. Furthermore, comparative numerical simulations were conducted on an Inverted Pendulum on a Cart system to benchmark the proposed Adaptive Neural Control against Linear Quadratic Regulator, Sliding Mode Control, and Nested Saturation Function controllers. Based on the Integral of Time-weighted Squared Error performance index, the Adaptive Neural Control demonstrated a significant reduction in control effort, achieving performance improvements of up to 95.02% compared to the aforementioned strategies.

This paper presents implementation of a single-neuron neural network to realize a adaptative PD control law for PVTOL system, in order to solve tracking trajectory problem. The proposed neural network updates its weights in real time through a simple learning algorithm, This allows PD control to be both adaptive and robust against external disturbances. The performance of the proposed controller is evaluated and compared to a linear state-feedback controller tuned by LQR method. The ITAE index performance is used to compare both control approaches. Numerical simulation results show that tracking trajectory error is reduced when using single-neuron neural network controller; however, due to training time, the energy cost of the control inputs is higher.