Dongping Li

This article examines a new family of (p,q)‐Laplacian type nonlinear fractional impulsive differential coupled equations involving both the ‐Caputo fractional derivative and –Riemann–Liouville fractional integral. With the help of Nehari manifold in critical point theory and fractional calculus properties, we obtain the existence of at least one nontrivial ground state solution for the coupled system with some natural and easily verifiable superlinear conditions on the nonlinearity.

In this paper, we propose an output feedback flight tracking control scheme for helicopter attitude and altitude systems with unmeasured states under full state constraints. Firstly, a state observer is constructed based on the measured output signals, which is proven to be rigorous since all states are constrained within the desired and assigned scopes. Secondly, the flight tracking controller is built using the state estimations with the full state constraints control method. Then, the Barrier Lyapunov function method is adopted to guarantee the stability of the composite closed-loop nonlinear error systems. Meanwhile, the linear matrix inequality technology is applied to calculate the gains of the state observer. Finally, a numerical simulation example is provided to confirm the reasonableness of the full state constraint output feedback flight tracking control method.

In this article, by combining a recent critical point theorem and several theories of the ψ-Caputo fractional operator, the multiplicity results of at least three distinct weak solutions are obtained for a new ψ-Caputo-type fractional differential system including the generalized p-Laplacian operator. It is noted that the nonlinear functions do not need to adapt certain asymptotic conditions in the paper, but, instead, are replaced by some simple algebraic conditions. Moreover, an evaluation criterion of the equation without solutions is also provided. Finally, two examples are given to demonstrate that the ψ-Caputo fractional operator is more accurate and can adapt to deal with complex system modeling problems by changing different weight functions.

In this paper, a full state-constrained anti-disturbance dynamic surface control method is proposed for six-degree-of-freedom unmanned helicopter systems under full state constraints and disturbances. Firstly, due to the underactuated characteristics of six-degree-of-freedom unmanned helicopter systems, an input–output feedback linearization method is used to transform the complex nonlinear systems into facilitated-control nonlinear ones. Based on the transformed systems, the nonlinear disturbance-observer-based control, backstepping control and Barrier Lyapunov function methods are used to construct the flight controller via uniting the state constraint control and dynamic surface control technologies. Then, Lyapunov stability theory is adopted for analysing the closed-loop tracking error systems, which confirms that the tracking errors are bounded under the proposed flight control scheme. Finally, a simulation in the MATLAB/Simulink environment verifies that the unmanned helicopter system can constrain all states under the action of the designed controller, with good dynamic performance.

In this paper, the Sturm-Liouville boundary value problem is studied for fractional differential equation with generalized (p, q)-Laplacian operator. By imposing mild assumptions on nonlinearity f, several new existence results of at least one or two nontrivial weak solutions are established through variational methods and critical point theorems. Furthermore, the criteria is also investigated for the nonexistence result.

In this brief, the output feedback control issue is investigated for linear systems under unmeasured states with the influences of measurement disturbances. Due to these unmeasured states, the measurement outputs are used for designing the controller, while, they are mixed with measurement disturbances. In order to construct the feedback controller, the states are observed using a state observer, which is driven via the measurement outputs. A disturbance observer is employed to estimate the measurement disturbances. Then, the linear matrix inequations technique is adopted for disposing the coupling between these observers. Furthermore, the Lyapunov stability theory is applied to prove the stability analysis of closed-loop systems. Finally, a numerical example is given to show the availability of proposed control method.